From d0bfdbf2ac287c210e774cf645c22dfca363fcd8 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Thu, 27 Feb 2020 10:51:53 +0100 Subject: [PATCH 001/117] Added many-valued context functions and quality of life improvements --- src/main/clojure/conexp/fca/contexts.clj | 3 +- src/main/clojure/conexp/fca/fast.clj | 23 ++++++++----- .../conexp/fca/many_valued_contexts.clj | 34 +++++++++++++++++++ 3 files changed, 50 insertions(+), 10 deletions(-) diff --git a/src/main/clojure/conexp/fca/contexts.clj b/src/main/clojure/conexp/fca/contexts.clj index 4c0a62f20..7de699f5d 100644 --- a/src/main/clojure/conexp/fca/contexts.clj +++ b/src/main/clojure/conexp/fca/contexts.clj @@ -490,7 +490,8 @@ [ctx] (make-context-nc (attributes ctx) (objects ctx) - (fn [[m g]] ((incidence ctx) [g m])))) + (fn ([[m g]] ((incidence ctx) [g m])) + ([m g] ((incidence ctx) [g m]))))) (defn invert-context "Inverts context ctx, that is (G,M,I) gets (G,M,(G x M) \\ I)." diff --git a/src/main/clojure/conexp/fca/fast.clj b/src/main/clojure/conexp/fca/fast.clj index 75caa5751..f7594c0f5 100644 --- a/src/main/clojure/conexp/fca/fast.clj +++ b/src/main/clojure/conexp/fca/fast.clj @@ -115,13 +115,18 @@ "Returns [object-vector, attribute-vector, object-count, attribute-count, incidence-matrix] of context with the obvious definitions." - [context] - (let [object-vector (vec (objects context)), - attribute-vector (vec (attributes context)), - object-count (count object-vector), - attribute-count (count attribute-vector), - incidence-matrix (to-binary-matrix object-vector attribute-vector (incidence context))] - [object-vector attribute-vector object-count attribute-count incidence-matrix])) + ([context] + (let [object-vector (vec (objects context)), + attribute-vector (vec (attributes context)), + object-count (count object-vector), + attribute-count (count attribute-vector), + incidence-matrix (to-binary-matrix object-vector attribute-vector (incidence context))] + [object-vector attribute-vector object-count attribute-count incidence-matrix])) + ([object-vector attribute-vector incidence] ;; if you need a specific order on the objects or attributes + (let [object-count (count object-vector) + attribute-count (count attribute-vector) + incidence-matrix (to-binary-matrix object-vector attribute-vector incidence)] + [object-vector attribute-vector object-count attribute-count incidence-matrix]))) (defmacro with-binary-context "For a given context defines object-vector, attribute-vector, @@ -129,7 +134,7 @@ way." [context & body] `(let [[~'object-vector ~'attribute-vector ~'object-count ~'attribute-count ~'incidence-matrix] - (to-binary-context ~context)] + (if (context? ~context) (to-binary-context ~context) ~context)] ~@body)) (defn bitwise-object-derivation @@ -155,7 +160,7 @@ ;;; Next Closure -(defn- bitwise-context-attribute-closure +(defn bitwise-context-attribute-closure "Computes the closure of A in the context given by the parameters." [^long object-count, ^long attribute-count, incidence-matrix, ^BitSet A] (let [^BitSet A (.clone A), diff --git a/src/main/clojure/conexp/fca/many_valued_contexts.clj b/src/main/clojure/conexp/fca/many_valued_contexts.clj index 9af7525bb..56744a482 100644 --- a/src/main/clojure/conexp/fca/many_valued_contexts.clj +++ b/src/main/clojure/conexp/fca/many_valued_contexts.clj @@ -159,6 +159,40 @@ (let [inz (incidence mv-ctx)] (set-of (inz [g m]) [m (attributes mv-ctx)]))) +(defn incidences-of-object + "For a given many-valued context mv-ctx and a given object g, + returns the set of all values of g in mv-ctx." + [mv-ctx g] + (when-not (contains? (objects mv-ctx) g) + (illegal-argument "Given element is not an object of the given many-valued context.")) + (apply merge + (map #(hash-map (get-in % [0 1]) (second %)) + (filter #(= g (get-in % [0 0])) + (incidence mv-ctx))))) + +(defn object-by-incidence + "For a given many-valued context mv-ctx and an attribute-value map, + returns all objects having these values." + [mv-ctx values] + (when-not (subset? (set (keys values)) (attributes mv-ctx)) + (illegal-argument "Values must only contain attributes of the context.")) + (set (filter #(every? (fn [a] (= ((incidences-of-object mv-ctx %) a) (values a))) (keys values)) + (objects mv-ctx)))) + +(defn make-mv-subcontext + "For a given many-valued context, returns the induced subcontext given + by the object and attribute set." + [mv-ctx objs attrs] + (when-not (and (subset? objs (objects mv-ctx)) + (subset? attrs (attributes mv-ctx))) + (illegal-argument "The attributes and objects have to be subsets + of the many-valued contexts attributes and objects.")) + (make-mv-context objs attrs + (apply merge + (map #(hash-map (first %) (second %)) + (filter #(and (contains? objs (get-in % [0 0])) + (contains? attrs (get-in % [0 1]))) + (apply list (incidence mv-ctx))))))) ;;; (defn scale-mv-context From 2217cd404a05d9620a90ad62f2e4d58978e2997b Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Thu, 27 Feb 2020 10:52:41 +0100 Subject: [PATCH 002/117] Conexp now with pq-cores --- src/main/clojure/conexp/fca/cores/cover.clj | 373 ++++++++++++++++++ src/main/clojure/conexp/fca/cores/pqcores.clj | 309 +++++++++++++++ .../clojure/conexp/fca/cores/cover_test.clj | 92 +++++ .../clojure/conexp/fca/cores/pqcores_test.clj | 88 +++++ 4 files changed, 862 insertions(+) create mode 100644 src/main/clojure/conexp/fca/cores/cover.clj create mode 100644 src/main/clojure/conexp/fca/cores/pqcores.clj create mode 100644 src/test/clojure/conexp/fca/cores/cover_test.clj create mode 100644 src/test/clojure/conexp/fca/cores/pqcores_test.clj diff --git a/src/main/clojure/conexp/fca/cores/cover.clj b/src/main/clojure/conexp/fca/cores/cover.clj new file mode 100644 index 000000000..58b9e41a6 --- /dev/null +++ b/src/main/clojure/conexp/fca/cores/cover.clj @@ -0,0 +1,373 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.cores.cover + (:require [conexp.base :exclude [next-closed-set]] + [conexp.fca.contexts :refer :all] + [conexp.fca.fast :refer + [next-closed-set to-hashset to-binary-context + bitwise-attribute-derivation forall-in-bitset + bitwise-object-derivation to-binary-matrix + bitwise-context-attribute-closure]] + [clojure.core.reducers :as r] + [clojure.set :refer :all]) + (:import [java.util BitSet])) + +;;;;;;;;;;;;;;;;;;;;; General Cover Methods ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; + +;;; merger +(defn cover-merger + "Merges two cover relations in dictionary format." + ([c1 c2] + (merge-with (partial merge-with into) c1 c2)) + ([c1] c1) ([] {})) + +(defn meet-irreducible-by-cover? + "This method checks if an element is meet irreducible in the cover + relation." + [element cover] + (>= 1 (count (:upper (get cover element))))) + +(defn join-irreducible-by-cover? + "This method checks if an element is meet irreducible in the cover + relation." + [element cover] + (>= 1 (count (:lower (get cover element))))) + + +;;;;;;;;;;;;;;;;;;;;; Cover Methods for Intents ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;;; comperator +(defn- subsetneq? + "Tests if 'a is a subset of 'b, but not equal." + [a b] + (and (not (= a b)) + (subset? a b))) + + +;;; Generate Cover Relation as Dictionary +(defn- direct-lower-neighbor? + "Checks if 'candidate is a direct lower neighbor of element in 'order" + [order candidate element] + (let [upper (get-in order [candidate :upper]) + next (filter #(subsetneq? % element) + upper)] + (empty? next))) + +(defn- find-lower-neighbors + "Finds all direct lower neighbors of element in 'cover." + [cover root element] + (loop [search #{root} lower-covers #{}] + (let [upper (r/reduce union #{} (for [e search] (get-in cover [e :upper]))) + next-search (filter #(subsetneq? % element) + upper) + direct-lower (filter #(direct-lower-neighbor? cover % element) + search)] + (if (empty? next-search) + (union direct-lower lower-covers) + (recur next-search (union direct-lower + lower-covers)))))) + +(defn- build-size-bucket-map + "This method groups all sets in base-set according to their + cardinality. These are returned as map." + [base-set] + (r/reduce (partial merge-with into) + (for [b base-set] {(count b) #{b}}))) + + +(defn- add-to-cover + "This method generates part of the cover structure. It generates a + map that includes 'element assigned with all it's lower + neighbors. Additionally, the map includes for each lower the + reference that 'element is it's upper neighbor." + [element lowers] + (let [adder {element {:lower (set lowers) :upper #{}}} + lower-updates + (r/reduce cover-merger + {} (for [l lowers] {l {:upper #{element}}}))] + (cover-merger adder lower-updates))) + +(defn generate-cover + "For a base-set containing set's of elements, this method computed the + cover relation of the subset order. The cover relation is returned + as a map which assigns each element of the base-set to it's direct + lower and upper neighbors in the following way: + + :element {:upper #{} :lower #{}}" + [base-set] + (let [buckets (build-size-bucket-map base-set) + sort-keys (sort (keys buckets)) + root (first (get buckets (first sort-keys))) + init-cover {root {:lower #{} :upper #{}}}] + (loop [rest-sort-keys (rest sort-keys) cover init-cover] + (if (empty? rest-sort-keys) + cover + (let [new-cover (r/reduce cover-merger cover + (pmap #(add-to-cover % (find-lower-neighbors cover root %)) + (get buckets (first rest-sort-keys))))] + (recur (rest rest-sort-keys) new-cover)))))) + +;;; Methods to update context changes in the cover relation + +;; object updates +(defn- into-but-supersets + "Inserts all element e of s2 into s1 if there exists no subset of e in s1" + [s1 s2] + (set (reduce (fn [s1 e] (if (some #(subsetneq? % e) s1) s1 + (conj s1 e))) s1 s2))) + +(defn- into-but-subsets + "Inserts all element e of s2 into s1 if there exists no superset of e in s1" + [s1 s2] + (set (reduce (fn [s1 e] (if (some #(subsetneq? e %) s1) s1 + (conj s1 e))) + s1 s2))) + +(defn reassign-cover + "This method removes an intent from the cover structure and updates + the cover relation's :lower and :upper assignments." + [cover intent] + (let [upper (:upper (get cover intent)) + lower (:lower (get cover intent)) + upper-updated (if (not (= 0 (count upper))) + (loop [cur (first upper) other (rest upper) cur-update cover] + (let [newCover (-> cur-update + (update-in [cur :lower] disj intent) + (update-in [cur :lower] into-but-subsets lower))] + (if (= 0 (count other)) newCover + (recur (first other) (rest other) newCover)))) + cover) + lower-updated (if (not (= 0 (count lower))) + (loop [cur (first lower) other (rest lower) cur-update upper-updated] + (let [newCover (-> cur-update + (update-in [cur :upper] disj intent) + (update-in [cur :upper] into-but-supersets upper))] + (if (= 0 (count other)) newCover + (recur (first other) (rest other) newCover)))) + upper-updated)] + (dissoc lower-updated intent))) + +(defn- update-cover + "Removes all intents of toRemove in the cover relation and update + all :lower and :upper assignments." + [toRemove cover] + (loop [cur (first toRemove) iterate (rest toRemove) updatedCover cover] + (if (= 0 (count iterate)) + (reassign-cover updatedCover cur) + (recur (first iterate) (rest iterate) (reassign-cover updatedCover cur))))) + +(defn- remove-if-meet-irreducible + "This method removes an element in the cover structure if it is meet + irreducible." + [element cover] + (if (meet-irreducible-by-cover? element cover) + (reassign-cover cover element) + cover)) + +(defn remove-meet-irreducible-lower-p + "This method removes all meet irreducible elements of the cover + structure with cardinality lower then p." + [cover p] + (let [k (reverse + (sort-by count (filter #(< (count %) p) (keys cover))))] + (if (= 0 (count k)) cover + (loop [cur (first k) other (rest k) updated cover] + (if (= 0 (count other)) + (remove-if-meet-irreducible cur updated) + (recur (first other) (rest other) (remove-if-meet-irreducible cur updated))))))) + +;; update attributes + +(defn- intersecter + "This is a helper method to update cover elements by + intersection. It intersects the element and all it's :lower + and :upper references with the new attr domain." + [element cover attr] + (let [newkey (intersection element attr) + newlower (disj (set (for [i (:lower cover)] (intersection attr i))) newkey) + newupper (disj (set (for [i (:upper cover)] (intersection attr i))) newkey)] + {newkey (assoc cover :lower newlower :upper newupper) })) + +(defn attribute-intersection-cover + "This methods updates the concept lattice cover relation on a change + of the attribute domain to a subset. For this the method intersects + all keys with the new attribute domain. Additionally, elements + which's intersection with 'attr are the same are merged." + [cover attr] + (let [toupdate (keys cover) + merger (fn [c1 c2] (merge-with (partial merge-with into) c1 c2))] + (loop [cur (first toupdate) other (rest toupdate) newcover {}] + (let [updated-newcover (merger newcover + (intersecter cur (get cover cur) attr))] + (if (= 0 (count other)) updated-newcover + (recur (first other) (rest other) updated-newcover)))))) + +;; faster attribute deleter +(defn- next-closed-set-iterator + "This method is a wrapper for the next-closed-set method in fast + fca. It returns the next closed set given 'start." + [[object-vector attribute-vector object-count attribute-count incidence-matrix] start] + (let [o-prime (partial bitwise-object-derivation incidence-matrix object-count attribute-count), + a-prime (partial bitwise-attribute-derivation incidence-matrix object-count attribute-count), + next (next-closed-set attribute-count + (partial bitwise-context-attribute-closure + object-count + attribute-count + incidence-matrix) + start)] + next)) + +(defn- find-all-updates + "This method determines all updates that need to be made to the attribute lattice." + [attribute-concepts cover] + (loop [cur (set attribute-concepts) toupdate (set attribute-concepts)] + (let [upper (future (set (reduce into #{} (pmap #(get-in cover [% :upper]) cur)))) + lower (set (pmap #(get-in cover [% :lower]) cur)) + nexttoupdate (r/reduce into toupdate (merge lower @upper))] + (if (empty? cur) + nexttoupdate + (recur @upper nexttoupdate))))) + +(defn attribute-deletion-cover + "This method updates the concept lattice given by cover on a + deletion of attributes in the context." + [cover old-ctx del-attributes] + (if (empty? del-attributes) cover + (let [prev-attributes (difference (attributes old-ctx) + del-attributes) + attr-order (into + (vec del-attributes) + (vec prev-attributes)) + obj-vec (vec (objects old-ctx)) + attr-count (count attr-order) + bin-incidence (to-binary-matrix obj-vec attr-order + (fn ([a b] ((incidence old-ctx) [a b])) + ([[a b]] ((incidence old-ctx) [a b])))) + bin-ctx [obj-vec attr-order (count obj-vec) attr-count bin-incidence] + attribute-concepts (for [i del-attributes] + (let [a (BitSet. attr-count)] + (.set a (.indexOf attr-order i)) + (to-hashset attr-order + (bitwise-context-attribute-closure (count obj-vec) (count attr-order) bin-incidence a)))) + toupdate (find-all-updates attribute-concepts cover)] + (loop [cur (first toupdate) other (rest toupdate) newcover {}] + (let [updated-newcover (cover-merger newcover (intersecter cur (get cover cur) prev-attributes))] + (if (= 0 (count other)) + (cover-merger (apply dissoc cover toupdate) updated-newcover) + (recur (first other) (rest other) updated-newcover))))))) + +;; general updater for intent covers +(defn cover-reducer + "This method updates the cover relation if the context changed to a + pq-core. For this it first updates the attribute domain. Secondly, + all meet irreducible intents with cardinality lower then p are + removed." + ([cover ctx core p] + (let [first-attr (if (not (= (attributes ctx) (attributes core))) + (attribute-deletion-cover cover ctx (difference (attributes ctx) (attributes core))) + cover) + second-objects (if (not (= (objects ctx) (objects core))) + (remove-meet-irreducible-lower-p first-attr p) + first-attr)] + second-objects))) + +;;;;;;;;;;;;;;;;;;;;; Cover Methods for Concepts ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;;; comperator +(defn- subconceptneq? + "Tests if 'a is a subset of 'b, but not equal." + [a b] + (and (not (= (first a) (first b))) (subset? (first a) (first b)))) + +;;; helper + +(defn- dual-entry + "This function swaps the extent and intent values of a cover entry." + [old-cover intent {extent :extent lower :lower upper :upper}] + (let [derive #(get-in old-cover [% :extent])] + {extent {:lower (set (map derive upper)) :upper (set (map derive lower)) :extent intent}})) + +(defn dual-concept-cover + "This method swaps the intents and extent entries in the concept + cover" + [cover] + (let [intents (keys cover)] + (r/reduce merge (r/map #(dual-entry cover % (get cover %)) intents)))) + +;;; generate +(defn generate-concept-cover + "For a base-set containing set's of elements, this method computed the + cover relation of the subconcept order. The cover relation is returned + as a map which assigns each concept of the base-set to it's direct + lower and upper neighbors in the following way: + + :intent {:upper {intent ..} :lower {intent ..} :extent #{}}" + [base-set] + (let [intents (map last base-set) + extent-map (future (r/fold (partial merge) + (r/map #(hash-map (second %) {:extent (first %)}) + base-set))) + intent-cover (future (generate-cover intents)) + concept-cover (merge-with into @intent-cover @extent-map)] + concept-cover)) + + +(defn- insert-as-root-concept + "This method inserts a concept into the cover relation." + [intent extent] + {intent {:lower #{} :upper #{} :extent extent}}) + +(defn insert-concept + "This method inserts a concept into the cover relation." + [cover intent extent] + (let [root-candidates (filter #(empty? (:lower (get cover %))) (keys cover)) + roots (filter #(subset? % intent) root-candidates) + inserted (cover-merger cover (insert-as-root-concept intent extent))] + (update (reduce cover-merger inserted + (for [root roots] + (add-to-cover intent (find-lower-neighbors inserted root intent)))) + intent #(assoc % :extent extent)))) + +(defn attribute-insertion-cover +"This method updates the concept lattice given by cover on an + insertion of attributes to the context. The added attributes are + already included in new-context and are further given by + new-attributes." + [cover new-ctx new-attributes] + (if (empty? new-attributes) cover + (let [prev-attributes (difference + (attributes new-ctx) + new-attributes) + attr-order (into + (vec new-attributes) + (vec prev-attributes)) + obj-vec (vec (objects new-ctx)) + bin-incidence (to-binary-matrix obj-vec attr-order + (fn ([a b] ((incidence new-ctx) [a b])) + ([[a b]] ((incidence new-ctx) [a b])))) + bin-ctx [obj-vec attr-order (count obj-vec) (count attr-order) bin-incidence] + start (BitSet.) + setter (.set start (count new-attributes) (count attr-order) true) + cur-lattice (agent cover) + bin-first-next (next-closed-set-iterator bin-ctx start)] + (if (nil? bin-first-next) cover + (loop [next (to-hashset attr-order bin-first-next) bin-next bin-first-next] + (let [old (intersection next prev-attributes)] + ;; async update cover + (send-off cur-lattice insert-concept next (attribute-derivation new-ctx next)) + + (send-off cur-lattice + #(if (= old + (to-hashset attr-order + (let [n (.clone bin-next) oldn (.and n start)] + (bitwise-context-attribute-closure (count obj-vec) (count attr-order) bin-incidence n)))) + % + (reassign-cover % old))) + (if (= next (attributes new-ctx)) + (do (await cur-lattice) @cur-lattice) + (let [bin-closure (next-closed-set-iterator bin-ctx bin-next)] + (recur (to-hashset attr-order bin-closure) bin-closure))))))))) diff --git a/src/main/clojure/conexp/fca/cores/pqcores.clj b/src/main/clojure/conexp/fca/cores/pqcores.clj new file mode 100644 index 000000000..3a053dae3 --- /dev/null +++ b/src/main/clojure/conexp/fca/cores/pqcores.clj @@ -0,0 +1,309 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.cores.pqcores + (:require [conexp.base :refer :all] + [conexp.fca.contexts :refer :all] + [conexp.fca.lattices :refer + [concept-lattice base-set]] + [conexp.fca.fast :as fast] + [conexp.fca.cores.cover :refer :all] + [clojure.core.reducers :as r])) + +;;; compute pq-core + +(defn pk-dense? + "This method tests if a context is pk-dense. Alternatively one can + check if an object/attribute has the minimum required derivation + size. + + A context is pk-dense iff it every object has a minimum derivation + size of p and every attribute has a minimum derivation size of k." + ([ctx p k] + (or (and (= (count (objects ctx)) 0) + (= (count (attributes ctx)) 0)) + (and (pk-dense? (objects ctx) ctx object-derivation p) + (pk-dense? (attributes ctx) ctx attribute-derivation k)))) + ([target ctx deri limit] + (not (some #(< (count (deri ctx (conj #{} %1))) limit) + target)))) + + +(defn- step-reduce-context + "This is the iterator for an iterative computation of the pq-core. It + computes a subcontext by removing all objects and attributes which + do not have the minimum derivation size in ctx." + [ctx p k] + (let [rel (if (set? (incidence ctx)) + (incidence ctx) + (filter (incidence ctx) + (for [o (objects ctx) a (attributes ctx)] [o a])))] + (make-context + (filter #(pk-dense? (conj #{} %1) ctx object-derivation p) + (objects ctx)) + (filter #(pk-dense? (conj #{} %1) ctx attribute-derivation k) + (attributes ctx)) + rel))) + + +(defn compute-core + "Computes the pq-core of a context ctx. + + The pk-core of a context ctx is the larges subcontext which is + pq-dense. Such a subcontext is unique for p,q in N" + [context p k] + (loop [ctx context] + (if (pk-dense? ctx p k) + ctx + (recur (step-reduce-context ctx p k))))) + +;;;; calculate all pq-core sizes + +(defn- ctx-core-size-fix-p-iterator + "For a fixed p this method computes the size of all pq-core with + q>=1. The size is measured as |G|*|M|" + [ctx last-k p] + (loop [core (compute-core ctx p 1) k 1 core-sizes []] + (let [attr-count (double (* (count (attributes core)) + (count (objects core)))) + new-core-sizes (conj core-sizes [p k attr-count])] + (if (= k last-k) + new-core-sizes + (recur (compute-core core p (inc k)) (inc k) new-core-sizes))))) + + +(defn ctx-core-sizes + "For a formal context computes the size of all pq-cores, which have at + least one object or attribute. This method considers only pq-cores + for p,q != 0, since otherwise there would be an infinite number of + p,q for which the core is not empty. A context's size is measured as + |G|*|M|. This method is parallelized over p. If your context + contains many more attributes, you might want to consider computing + this for the dual context. + + The sizes are returned as a list of triples [p q size]." + [ctx] + (let [p (->> ctx objects (map (partial conj #{})) + (map (comp count (partial object-derivation ctx))) + sort last range (map inc)) + last-k (->> ctx attributes (map (partial conj #{})) + (map (comp count (partial attribute-derivation ctx))) + (apply max))] + (reduce (partial apply conj) + (pmap (partial ctx-core-size-fix-p-iterator ctx last-k) p)))) + +;;; calculate all pq-core lattice sizes + +(defn- ctx-core-lattice-size-fix-p-iterator-cover + "For a fixed p this method computes the size of all pq-core concept + lattices with q in k-range. 'init-intents is the cover relation of + all concept intents." + [ctx init-intends k-range p] + (loop [last-core nil + core (compute-core ctx p (first k-range)) + k k-range + core-sizes [] + last-intends (cover-reducer init-intends ctx core p)] + (let [l-count (count (keys last-intends)) + new-core-sizes (if (empty? k) core-sizes + (conj core-sizes [p (first k) l-count]))] + (if (empty? (rest k)) + new-core-sizes + (let [next-k (apply min (last k) + (map #(count (attribute-derivation core #{%})) + (attributes core))) + next-core (compute-core core p (inc next-k)) + ahead-core-sizes (into new-core-sizes (for [i (range (second k) (inc next-k))] [p i l-count]))] + (recur core next-core (range (inc next-k) (inc (last k))) + ahead-core-sizes (cover-reducer last-intends core next-core p))))))) + +(defn core-lattice-sizes + "For a formal context computes the size of all pq-cores concept + lattices, which have at least one object or attribute. This method + considers only pq-cores for p,q != 0, since otherwise there would be + an infinite number of p,q for which the core is not empty. This + method is parallelized over p. If your context contains many more + attributes, you might want to consider computing this for the dual + context. For very large contexts you can all pq-cores with p> ctx objects (map (partial conj #{})) + (map (comp count (partial object-derivation ctx))) + sort last range (map inc)) + k-range (->> ctx attributes (map (partial conj #{})) + (map (comp count (partial attribute-derivation ctx))) + (apply max) range (map inc)) + init-lattice (doall (->> ctx concept-lattice base-set (map last) generate-cover))] + (vec (reduce (partial apply conj) + (pmap (partial ctx-core-lattice-size-fix-p-iterator-cover ctx init-lattice k-range) + p))))) + ([ctx x y] + (let [p (->> ctx objects (map (partial conj #{})) + (map (comp count (partial object-derivation ctx))) + sort last range (map inc)) + last-k (->> ctx attributes (map (partial conj #{})) + (map (comp count (partial attribute-derivation ctx))) + (apply max)) + init-lattice-1-y (future (doall (->> (compute-core ctx 1 y) concept-lattice base-set (map last) generate-cover))) + init-lattice-x-1 (future (doall (->> (compute-core ctx x 1) concept-lattice base-set (map last) generate-cover)))] + (vec (into (for [i (range x) j (range y)] [i j 0]) + (reduce (partial apply conj) + (pmap (partial apply ctx-core-lattice-size-fix-p-iterator-cover ctx) + (map #(if (< % x) [@init-lattice-1-y (range y last-k) %] [@init-lattice-x-1 (range 1 last-k) %]) + p)))))))) + +;;; find first object and attribute core for given maximal concept lattice size + +(defn find-size-core + "Returns the minimum p,q such that the 1,q- and p,1-core have a + concept lattice size of 'size." + [ctx size] + (let [;; max derivation size for q + last-possible-q (->> ctx attributes (map (partial conj #{})) + (map (comp count (partial attribute-derivation ctx))) + (apply max)) + ;; max derivation size for p + last-possible-p (->> ctx objects (map (partial conj #{})) + (map (comp count (partial object-derivation ctx))) + (apply max)) + + ;; binary search for minimum q, such that the 1,q-core has a + ;; maximum concept lattice size of 'size + p (future (loop [core (compute-core ctx (* 3 (int (/ last-possible-p 4))) 1) + curp (* 3 (int (/ last-possible-p 4))) lastp 1 maxp last-possible-p] + (if (or (= curp maxp) (= curp lastp)) + curp + (let [ccount (count (fast/concepts core))] + (if (> ccount size ) + (recur (compute-core ctx (int (/ (+ maxp curp) 2)) 1) + (int (/ (+ maxp curp) 2)) curp maxp) + (if (> (count (fast/concepts (compute-core ctx (- curp 1) 1))) size) + curp + (recur (compute-core ctx (int (/ (+ lastp curp) 2)) 1) + (int (/ (+ lastp curp) 2)) lastp curp))))))) + ;; binary search for minimum q, such that the 1,q-core has a + ;; maximum concept lattice size of 'size + q (future (loop [core (compute-core ctx 1 (* 3 (int (/ last-possible-q 4)))) + current-q (* 3 (int (/ last-possible-q 4))) latest-q 1 maximum-q last-possible-q] + (if (or (= current-q maximum-q) (= current-q latest-q)) current-q + (let [ccount (count (fast/concepts core))] + (if (> ccount size ) + (recur (compute-core ctx 1 (int (/ (+ maximum-q current-q) 2)) ) + (int (/ (+ maximum-q current-q) 2)) current-q maximum-q) + (if (> (count (fast/concepts (compute-core ctx 1 (- current-q 1)))) size) + current-q + (recur (compute-core ctx 1 (int (/ (+ latest-q current-q) 2))) + (int (/ (+ latest-q current-q) 2)) latest-q current-q)))))))] + [@p @q])) + +(defn large-ctx-lattice-sizes-partial + "This method computes the context lattice sizes for all cores of + 'ctx. The core lattice sizes computed are also core of the largest + object core or attribute core of size at most k." + [ctx k] + (apply core-lattice-sizes ctx (find-size-core ctx))) + +;;; general transformer + +(defn transform-bv + "Transforms the concept lattice of ctx1 to that of ctx2 using the + algorithm presented in .. The methods input are the two contexts and + the concept lattice of ctx1 as cover relation generated by + cover.clj. For ctx1 and ctx2 it required that there exists a super + context ctx such that ctx1 and ctx2 are induced subcontexts of ctx. + + This method is useful for larger contexts ctx1 and ctx2 which have + many objects and attributes in common." + [ctx1 ctx2 bv1] + (let [;; update the set of attributes of the ctx and bv first + shared-attributes (intersection (attributes ctx2) (attributes ctx1)) + remove-ctx1-attributes-bv (attribute-deletion-cover bv1 ctx1 (difference (attributes ctx1) shared-attributes)) + ctx2-only-attributes (difference (attributes ctx2) (attributes ctx1)) + attr-intermediate-ctx (make-context (objects ctx1) (attributes ctx2) + (fn [a b] (if (contains? (objects ctx2) a) + ((incidence ctx2) [a b]) + ((incidence ctx1) [a b])))) + insert-ctx2-attributes-bv (attribute-insertion-cover remove-ctx1-attributes-bv attr-intermediate-ctx ctx2-only-attributes) + ;; To update all objects, we update the attributes of the dual + ;; context + dual-bv (dual-concept-cover insert-ctx2-attributes-bv) + shared-objects (intersection (objects ctx1) (objects ctx2)) + dual-ctx (dual-context attr-intermediate-ctx) + remove-ctx1-objects-bv (attribute-deletion-cover + dual-bv (make-context shared-objects (attributes dual-ctx) (incidence dual-ctx)) + (difference (objects ctx1) shared-objects)) + ctx2-only-objects (difference (objects ctx2) (objects ctx1)) + insert-ctx2-objects-bv (attribute-insertion-cover remove-ctx1-objects-bv (dual-context ctx2) ctx2-only-objects)] + (dual-concept-cover insert-ctx2-objects-bv))) + +(defn transform-bv-subctx + "Transforms the concept lattice of ctx1 to that of ctx2 using the + algorithm presented in .. The methods input are the two contexts and + the concept lattice of ctx1 as cover relation generated by + cover.clj. For ctx1 and ctx2 it required that ctx2 is a subcontext of ctx1 + + This method is useful for larger contexts ctx1 and ctx2 which have + many objects and attributes in common." + [ctx1 ctx2 bv1] + (let [;; update the set of attributes of the ctx and bv first + shared-attributes (attributes ctx2) + remove-ctx1-attributes-bv (attribute-intersection-cover bv1 shared-attributes) + + ;; To update all objects, we update the attributes of the dual + ;; context + dual-bv (dual-concept-cover remove-ctx1-attributes-bv) + shared-objects (objects ctx2) + remove-ctx1-objects-bv (attribute-intersection-cover dual-bv shared-objects)] + (dual-concept-cover remove-ctx1-objects-bv))) + +(defn transform-bv-intents-cores + "Transforms the intent lattice of ctx1 to that of ctx2 using the + algorithm presented in .. The methods input are the two contexts and + the concept lattice of ctx1 as cover relation generated by + cover.clj. For ctx1 and ctx2 it required that ctx2 is a pkcore of ctx1. + + This method is useful for larger contexts ctx1 and ctx2 which have + many objects and attributes in common." + [ctx1 core bv1 p] + (cover-reducer ctx1 core p)) + +(defn transform-bv-inserted-attribute-only + "Transforms the concept lattice of ctx1 to that of ctx2 using the + algorithm presented in .. The methods input are the two contexts and + the concept lattice of ctx1 as cover relation generated by + cover.clj. For ctx1 and ctx2 it required that ctx1 is a subcontext + of ctx2 and they have the same set of objects. + + This method is useful for larger contexts ctx1 and ctx2 which have + many objects and attributes in common." + [ctx1 ctx2 bv1] + (let [;; update the set of attributes of the ctx and bv first + ctx2-only-attributes (difference (attributes ctx2) (attributes ctx1)) + attr-intermediate-ctx (make-context (objects ctx1) (attributes ctx2) + (fn [a b] (if (contains? (objects ctx2) a) + ((incidence ctx2) [a b]) + ((incidence ctx1) [a b])))) + insert-ctx2-attributes-bv (attribute-insertion-cover bv1 attr-intermediate-ctx ctx2-only-attributes)] + insert-ctx2-attributes-bv)) + +(defn transform-bv-deleted-attribute-only +"Transforms the concept lattice of ctx1 to that of ctx2 using the + algorithm presented in .. The methods input are the two contexts and + the concept lattice of ctx1 as cover relation generated by + cover.clj. For ctx1 and ctx2 it required that ctx2 is a subcontext + of ctx1 and has the same set of objects. + + This method is useful for larger contexts ctx1 and ctx2 which have + many objects and attributes in common." + [ctx1 ctx2 bv1] + (let [;; update the set of attributes of the ctx and bv first + shared-attributes (attributes ctx2) + remove-ctx1-attributes-bv (attribute-intersection-cover bv1 shared-attributes)] + remove-ctx1-attributes-bv)) diff --git a/src/test/clojure/conexp/fca/cores/cover_test.clj b/src/test/clojure/conexp/fca/cores/cover_test.clj new file mode 100644 index 000000000..6564de236 --- /dev/null +++ b/src/test/clojure/conexp/fca/cores/cover_test.clj @@ -0,0 +1,92 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.cores.cover-test + (:use conexp.fca.cores.pqcores conexp.fca.cores.cover + conexp.fca.contexts) + (:use conexp.fca.contexts) + (:use clojure.test clojure.set)) + +(deftest test-generate-cover + (let [ctx (make-context (range 5) (range 5) <=) + cover (generate-cover (map last (concepts ctx)))] + (is (map? cover)) + (is (every? set? (keys cover))) + (is (every? map? (vals cover))) + (is (every? #((get cover %) :lower) + (keys cover))) + (is (every? #(contains? (get cover %) :upper) + (keys cover))))) + +(deftest test-generate-concept-cover + (let [ctx (make-context (range 5) (range 5) <=) + cover (generate-concept-cover (concepts ctx))] + (is (map? + cover)) + (is (every? set? + (keys cover))) + (is (every? map? + (vals cover))) + (is (every? #((get cover %) :lower) + (keys cover))) + (is (every? #(contains? (get cover %) :upper) + (keys cover))) + (is (every? #((get cover %) :extent) + (keys cover))) + (is (every? #(= (attribute-derivation ctx %) + (get-in cover [% :extent])) + (keys cover))))) + +(deftest test-dual-concept-cover + (let [ctx (make-context (range 5) (range 5) <=) + cover (generate-concept-cover (concepts ctx))] + (is (= (dual-concept-cover cover) + (generate-concept-cover (concepts (dual-context ctx))))))) + +(deftest test-irreducible + (let [ctx (make-context (range 5) (range 5) <=) + cover (generate-concept-cover (concepts ctx))] + (is (= 5 + (count (filter #(meet-irreducible-by-cover? % cover) (keys cover))))) + (is (= 5 + (count (filter #(join-irreducible-by-cover? % cover) (keys cover))))))) + +(deftest test-attribute-intersection-cover + (let [ctx (make-context (range 5) (range 5) <=) + cover (generate-cover (map last (concepts ctx))) + new-ctx (make-context (range 5) (range 3) <=) + new-cover (generate-cover (map last (concepts new-ctx)))] + (is (= new-cover + (attribute-intersection-cover cover (attributes new-ctx)))))) + +(deftest test-attribute-deletion-cover + (let [ctx (make-context (range 5) (range 5) <=) + cover (generate-cover (map last (concepts ctx))) + new-ctx (make-context (range 5) (attributes (compute-core ctx 2 3)) <=) + new-cover (generate-cover (map last (concepts new-ctx)))] + (is (= new-cover + (attribute-deletion-cover cover ctx (difference + (attributes ctx) + (attributes new-ctx))))))) + +(deftest test-attribute-insertion-cover + (let [ctx (make-context (range 5) (range 5) <=) + cover (generate-concept-cover (concepts ctx)) + new-ctx (make-context (range 5) (range 7) <=) + new-cover (generate-concept-cover (concepts new-ctx)) + gen-cover (attribute-insertion-cover cover new-ctx #{5 6})] + (is (= new-cover + gen-cover)))) + +(deftest test-cover-reducer + (let [ctx (make-context (range 10) (range 10) <=) + cover (generate-cover (map last (concepts ctx))) + new-ctx (compute-core ctx 4 6) + new-cover (generate-cover (map last (concepts new-ctx)))] + (is (= new-cover + (cover-reducer cover ctx new-ctx 4))))) diff --git a/src/test/clojure/conexp/fca/cores/pqcores_test.clj b/src/test/clojure/conexp/fca/cores/pqcores_test.clj new file mode 100644 index 000000000..ac8623851 --- /dev/null +++ b/src/test/clojure/conexp/fca/cores/pqcores_test.clj @@ -0,0 +1,88 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.cores.pqcores-test + (:use conexp.fca.cores.pqcores conexp.fca.cores.cover) + (:use conexp.fca.contexts) + (:use clojure.test)) + +(def empty-ctx (make-context #{} #{} #{})) + +(deftest test-pk-dense + (is (not (pk-dense? + (make-context (range 2) (range 2) <=) + 2 2))) + (is (pk-dense? + (make-context (range 1) (range 2) <=) + 2 1)) + (is (pk-dense? + [0] (make-context (range 1) (range 2) <=) + object-derivation 2)) + (is (pk-dense? + [1] (make-context (range 1) (range 2) <=) + attribute-derivation 1))) + +(deftest test-compute-core + (is (= (compute-core (make-context (range 5) (range 5) <=) 2 2) + (make-context (range 4) (range 1 5) <=))) + (is (= (compute-core (make-context (range 5) (range 5) =) 2 1) + empty-ctx))) + +(deftest test-ctx-core-sizes + (let [ctx (make-context (range 5) (range 5) <=) + sizes (ctx-core-sizes ctx)] + (is (= (count sizes) + (* (-> ctx objects count) + (-> ctx attributes count)))) + (is (every? double? (map last sizes))) + (is (= 190 + (int (reduce + (map last sizes))))))) + +(deftest test-ctx-lattice-sizes + (let [ctx (make-context (range 5) (range 5) <=) + sizes (core-lattice-sizes ctx) + plimit 3 klimit 3 + sizespk (core-lattice-sizes ctx plimit klimit) + example (nth sizes 7)] + (is (= (count sizes) + (* (-> ctx objects count) + (-> ctx attributes count)))) + (is (every? int? (map last sizes))) + (is (= 35 + (int (reduce + (map last sizes))))) + (is (= (count (concepts (compute-core ctx (first example) (second example)))) + (last example))) + (is (every? #(= 0 (last %)) + (filter #(and (> plimit (first %)) + (> klimit (second %))) + sizespk))))) + +(deftest test-find-size-core + (let [ctx (make-context (range 10) (range 10) <=) + [p q] (find-size-core ctx 3)] + (is (>= 3 + (count (concepts (compute-core ctx p 1))))) + (is (>= 3 + (count (concepts (compute-core ctx 1 q))))) + (is (< 3 + (count (concepts (compute-core ctx (dec p) 1))))) + (is (< 3 + (count (concepts (compute-core ctx 1 (dec q)))))))) + +(deftest test-transform-bv + (let [ctx1 (make-context (range 5) (range 5) <=) +; ctx2 (make-context (range 3 7) (range 3 7) <=) +; ctx3 (make-context (range 3) (range 3) <=) + ctx4 (make-context (range 7) (range 7) <=) + bv1 (generate-concept-cover (concepts ctx1)) +; bv2 (generate-concept-cover (concepts ctx2)) +; bv3 (generate-concept-cover (concepts ctx3)) + bv4 (generate-concept-cover (concepts ctx4))] +; (is (= (transform-bv ctx1 ctx2 bv1) bv2)) +; (is (= (transform-bv ctx1 ctx3 bv1) bv3)) + (is (= (transform-bv ctx1 ctx4 bv1) bv4)))) From 5392693764d0b850f880a4548dc16c85fea288a9 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Thu, 27 Feb 2020 14:11:26 +0100 Subject: [PATCH 003/117] moved files --- src/main/clojure/conexp/fca/{cores => }/cover.clj | 0 src/main/clojure/conexp/fca/{cores => }/pqcores.clj | 0 src/test/clojure/conexp/fca/{cores => }/cover_test.clj | 0 src/test/clojure/conexp/fca/{cores => }/pqcores_test.clj | 0 4 files changed, 0 insertions(+), 0 deletions(-) rename src/main/clojure/conexp/fca/{cores => }/cover.clj (100%) rename src/main/clojure/conexp/fca/{cores => }/pqcores.clj (100%) rename src/test/clojure/conexp/fca/{cores => }/cover_test.clj (100%) rename src/test/clojure/conexp/fca/{cores => }/pqcores_test.clj (100%) diff --git a/src/main/clojure/conexp/fca/cores/cover.clj b/src/main/clojure/conexp/fca/cover.clj similarity index 100% rename from src/main/clojure/conexp/fca/cores/cover.clj rename to src/main/clojure/conexp/fca/cover.clj diff --git a/src/main/clojure/conexp/fca/cores/pqcores.clj b/src/main/clojure/conexp/fca/pqcores.clj similarity index 100% rename from src/main/clojure/conexp/fca/cores/pqcores.clj rename to src/main/clojure/conexp/fca/pqcores.clj diff --git a/src/test/clojure/conexp/fca/cores/cover_test.clj b/src/test/clojure/conexp/fca/cover_test.clj similarity index 100% rename from src/test/clojure/conexp/fca/cores/cover_test.clj rename to src/test/clojure/conexp/fca/cover_test.clj diff --git a/src/test/clojure/conexp/fca/cores/pqcores_test.clj b/src/test/clojure/conexp/fca/pqcores_test.clj similarity index 100% rename from src/test/clojure/conexp/fca/cores/pqcores_test.clj rename to src/test/clojure/conexp/fca/pqcores_test.clj From 187f72f35f67b1879eeacde08344beaa26157dd6 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Thu, 27 Feb 2020 14:12:37 +0100 Subject: [PATCH 004/117] renamed namespaces --- src/main/clojure/conexp/fca/cover.clj | 2 +- src/main/clojure/conexp/fca/pqcores.clj | 2 +- src/test/clojure/conexp/fca/cover_test.clj | 4 ++-- src/test/clojure/conexp/fca/pqcores_test.clj | 2 +- 4 files changed, 5 insertions(+), 5 deletions(-) diff --git a/src/main/clojure/conexp/fca/cover.clj b/src/main/clojure/conexp/fca/cover.clj index 58b9e41a6..7ad5a022e 100644 --- a/src/main/clojure/conexp/fca/cover.clj +++ b/src/main/clojure/conexp/fca/cover.clj @@ -6,7 +6,7 @@ ;; the terms of this license. ;; You must not remove this notice, or any other, from this software. -(ns conexp.fca.cores.cover +(ns conexp.fca.cover (:require [conexp.base :exclude [next-closed-set]] [conexp.fca.contexts :refer :all] [conexp.fca.fast :refer diff --git a/src/main/clojure/conexp/fca/pqcores.clj b/src/main/clojure/conexp/fca/pqcores.clj index 3a053dae3..3394876e2 100644 --- a/src/main/clojure/conexp/fca/pqcores.clj +++ b/src/main/clojure/conexp/fca/pqcores.clj @@ -6,7 +6,7 @@ ;; the terms of this license. ;; You must not remove this notice, or any other, from this software. -(ns conexp.fca.cores.pqcores +(ns conexp.fca.pqcores (:require [conexp.base :refer :all] [conexp.fca.contexts :refer :all] [conexp.fca.lattices :refer diff --git a/src/test/clojure/conexp/fca/cover_test.clj b/src/test/clojure/conexp/fca/cover_test.clj index 6564de236..75e48bddb 100644 --- a/src/test/clojure/conexp/fca/cover_test.clj +++ b/src/test/clojure/conexp/fca/cover_test.clj @@ -6,8 +6,8 @@ ;; the terms of this license. ;; You must not remove this notice, or any other, from this software. -(ns conexp.fca.cores.cover-test - (:use conexp.fca.cores.pqcores conexp.fca.cores.cover +(ns conexp.fca.cover-test + (:use conexp.fca.pqcores conexp.fca.cover conexp.fca.contexts) (:use conexp.fca.contexts) (:use clojure.test clojure.set)) diff --git a/src/test/clojure/conexp/fca/pqcores_test.clj b/src/test/clojure/conexp/fca/pqcores_test.clj index ac8623851..17af1bd3d 100644 --- a/src/test/clojure/conexp/fca/pqcores_test.clj +++ b/src/test/clojure/conexp/fca/pqcores_test.clj @@ -6,7 +6,7 @@ ;; the terms of this license. ;; You must not remove this notice, or any other, from this software. -(ns conexp.fca.cores.pqcores-test +(ns conexp.fca.pqcores-test (:use conexp.fca.cores.pqcores conexp.fca.cores.cover) (:use conexp.fca.contexts) (:use clojure.test)) From 482a9e6b2e40c8fe76b852e16df51472951dad73 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Thu, 27 Feb 2020 14:22:05 +0100 Subject: [PATCH 005/117] moved subconcept function --- src/main/clojure/conexp/fca/contexts.clj | 10 ++++++++++ src/main/clojure/conexp/fca/cover.clj | 6 ------ src/main/clojure/conexp/fca/pqcores.clj | 2 +- src/test/clojure/conexp/fca/pqcores_test.clj | 2 +- 4 files changed, 12 insertions(+), 8 deletions(-) diff --git a/src/main/clojure/conexp/fca/contexts.clj b/src/main/clojure/conexp/fca/contexts.clj index 7de699f5d..34e31c465 100644 --- a/src/main/clojure/conexp/fca/contexts.clj +++ b/src/main/clojure/conexp/fca/contexts.clj @@ -764,6 +764,16 @@ (disj min-attrs m) neighbours)))))) +(defn subconcept? + "Tests if 'a is a subset of 'b, but not equal." + [a b] + (subset? (first a) (first b))) + +(defn subconceptneq? + "Tests if 'a is a subset of 'b, but not equal." + [a b] + (and (not (= (first a) (first b))) (subconcept? a b))) + ;;; Compatible Subcontexts diff --git a/src/main/clojure/conexp/fca/cover.clj b/src/main/clojure/conexp/fca/cover.clj index 7ad5a022e..410371830 100644 --- a/src/main/clojure/conexp/fca/cover.clj +++ b/src/main/clojure/conexp/fca/cover.clj @@ -277,12 +277,6 @@ second-objects))) ;;;;;;;;;;;;;;;;;;;;; Cover Methods for Concepts ;;;;;;;;;;;;;;;;;;;;;;;;;;;;; -;;; comperator -(defn- subconceptneq? - "Tests if 'a is a subset of 'b, but not equal." - [a b] - (and (not (= (first a) (first b))) (subset? (first a) (first b)))) - ;;; helper (defn- dual-entry diff --git a/src/main/clojure/conexp/fca/pqcores.clj b/src/main/clojure/conexp/fca/pqcores.clj index 3394876e2..38f10bff8 100644 --- a/src/main/clojure/conexp/fca/pqcores.clj +++ b/src/main/clojure/conexp/fca/pqcores.clj @@ -12,7 +12,7 @@ [conexp.fca.lattices :refer [concept-lattice base-set]] [conexp.fca.fast :as fast] - [conexp.fca.cores.cover :refer :all] + [conexp.fca.cover :refer :all] [clojure.core.reducers :as r])) ;;; compute pq-core diff --git a/src/test/clojure/conexp/fca/pqcores_test.clj b/src/test/clojure/conexp/fca/pqcores_test.clj index 17af1bd3d..d266ba496 100644 --- a/src/test/clojure/conexp/fca/pqcores_test.clj +++ b/src/test/clojure/conexp/fca/pqcores_test.clj @@ -7,7 +7,7 @@ ;; You must not remove this notice, or any other, from this software. (ns conexp.fca.pqcores-test - (:use conexp.fca.cores.pqcores conexp.fca.cores.cover) + (:use conexp.fca.pqcores conexp.fca.cover) (:use conexp.fca.contexts) (:use clojure.test)) From b166ff31a3ea3f2cdf064852c1f2d08963a2f0bb Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Thu, 27 Feb 2020 14:32:44 +0100 Subject: [PATCH 006/117] fixed comments and removed two duplicate functions --- src/main/clojure/conexp/fca/pqcores.clj | 57 ++++++------------------- 1 file changed, 13 insertions(+), 44 deletions(-) diff --git a/src/main/clojure/conexp/fca/pqcores.clj b/src/main/clojure/conexp/fca/pqcores.clj index 38f10bff8..9c0272f8b 100644 --- a/src/main/clojure/conexp/fca/pqcores.clj +++ b/src/main/clojure/conexp/fca/pqcores.clj @@ -214,10 +214,11 @@ (defn transform-bv "Transforms the concept lattice of ctx1 to that of ctx2 using the - algorithm presented in .. The methods input are the two contexts and - the concept lattice of ctx1 as cover relation generated by - cover.clj. For ctx1 and ctx2 it required that there exists a super - context ctx such that ctx1 and ctx2 are induced subcontexts of ctx. + algorithm presented in 'Knowledge Cores in Large Formal Contexts' + The methods input are the two contexts and the concept lattice of + ctx1 as cover relation generated by cover.clj. For ctx1 and ctx2 it + required that there exists a super context ctx such that ctx1 and + ctx2 are induced subcontexts of ctx. This method is useful for larger contexts ctx1 and ctx2 which have many objects and attributes in common." @@ -245,9 +246,10 @@ (defn transform-bv-subctx "Transforms the concept lattice of ctx1 to that of ctx2 using the - algorithm presented in .. The methods input are the two contexts and - the concept lattice of ctx1 as cover relation generated by - cover.clj. For ctx1 and ctx2 it required that ctx2 is a subcontext of ctx1 + algorithm presented in 'Knowledge Cores in Large Formal Contexts' + The methods input are the two contexts and the concept lattice of + ctx1 as cover relation generated by cover.clj. For ctx1 and ctx2 it + required that ctx2 is a subcontext of ctx1 This method is useful for larger contexts ctx1 and ctx2 which have many objects and attributes in common." @@ -265,45 +267,12 @@ (defn transform-bv-intents-cores "Transforms the intent lattice of ctx1 to that of ctx2 using the - algorithm presented in .. The methods input are the two contexts and - the concept lattice of ctx1 as cover relation generated by - cover.clj. For ctx1 and ctx2 it required that ctx2 is a pkcore of ctx1. + algorithm presented in 'Knowledge Cores in Large Formal Contexts' + The methods input are the two contexts and the concept lattice of + ctx1 as cover relation generated by cover.clj. For ctx1 and ctx2 it + required that ctx2 is a pkcore of ctx1. This method is useful for larger contexts ctx1 and ctx2 which have many objects and attributes in common." [ctx1 core bv1 p] (cover-reducer ctx1 core p)) - -(defn transform-bv-inserted-attribute-only - "Transforms the concept lattice of ctx1 to that of ctx2 using the - algorithm presented in .. The methods input are the two contexts and - the concept lattice of ctx1 as cover relation generated by - cover.clj. For ctx1 and ctx2 it required that ctx1 is a subcontext - of ctx2 and they have the same set of objects. - - This method is useful for larger contexts ctx1 and ctx2 which have - many objects and attributes in common." - [ctx1 ctx2 bv1] - (let [;; update the set of attributes of the ctx and bv first - ctx2-only-attributes (difference (attributes ctx2) (attributes ctx1)) - attr-intermediate-ctx (make-context (objects ctx1) (attributes ctx2) - (fn [a b] (if (contains? (objects ctx2) a) - ((incidence ctx2) [a b]) - ((incidence ctx1) [a b])))) - insert-ctx2-attributes-bv (attribute-insertion-cover bv1 attr-intermediate-ctx ctx2-only-attributes)] - insert-ctx2-attributes-bv)) - -(defn transform-bv-deleted-attribute-only -"Transforms the concept lattice of ctx1 to that of ctx2 using the - algorithm presented in .. The methods input are the two contexts and - the concept lattice of ctx1 as cover relation generated by - cover.clj. For ctx1 and ctx2 it required that ctx2 is a subcontext - of ctx1 and has the same set of objects. - - This method is useful for larger contexts ctx1 and ctx2 which have - many objects and attributes in common." - [ctx1 ctx2 bv1] - (let [;; update the set of attributes of the ctx and bv first - shared-attributes (attributes ctx2) - remove-ctx1-attributes-bv (attribute-intersection-cover bv1 shared-attributes)] - remove-ctx1-attributes-bv)) From 59ff2929ce1c069822646882644a2fbfc4020533 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Fri, 28 Feb 2020 10:58:47 +0100 Subject: [PATCH 007/117] Added Author Field --- AUTHORS.md | 1 + 1 file changed, 1 insertion(+) diff --git a/AUTHORS.md b/AUTHORS.md index 5b6cbc75b..f736206c9 100644 --- a/AUTHORS.md +++ b/AUTHORS.md @@ -13,3 +13,4 @@ Additional Contributors are * Anselm von Wangenheim (DimDraw) * Johannes Wollbold (bug reports, feature requests) * Sebastian Benner (API) +* Johannes Hirth (pq-cores) From 2ba13b4630104d1a10696b959026ad5c76495d8c Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 3 Mar 2020 14:39:05 +0100 Subject: [PATCH 008/117] base functionality for smeasures --- src/main/clojure/conexp/fca/smeasure.clj | 70 ++++++++++++++++++++++++ 1 file changed, 70 insertions(+) create mode 100644 src/main/clojure/conexp/fca/smeasure.clj diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj new file mode 100644 index 000000000..f048512d3 --- /dev/null +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -0,0 +1,70 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.smeasure + (:require [conexp.base :refer :all] + [conexp.fca.contexts :refer :all])) + +(defprotocol Smeasure + (context [sm] "Returns the original context that is measured.") + (scale [sm] "Returns the scale that measures the context.") + (measure [sm] "Returns the scale measure map that associates objects of context with objects of scale.")) + +(deftype ScaleMeasure [context scale measure] + Object + (equals [this other] + (and (= (class this) (class other)) + (= (.context this) (.context ^ScaleMeasure other)) + (every? #(= ((.measure this) %) + ((.measure ^ScaleMeasure other) %)) + (objects context)))) + (hashCode [this] + (hash-combine-hash ScaleMeasure context scale measure)) + ;; + Smeasure + (context [this] context) + (scale [this] scale) + (measure [this] measure)) + +(defn make-smeasure-nc [ctx scale m] + (ScaleMeasure. ctx scale m)) + +(defn- pre-image-measure + "Returns the pre-image map of a scale measures function." + [sm] + (let [m (measure sm)] + (if (map? m) + (apply (partial merge-with into) {} + (for [[k v] m] {v #{k}})) + (let [mapified (into {} + (for [obj (objects (context sm))] + [obj ((measure sm) obj)]))] + (apply (partial merge-with into) {} + (for [[k v] mapified] {v #{k}})))))) + +(defn original-extents [sm] + (let [scale-extents (extents (scale sm)) + pre-image (pre-image-measure sm)] + (map #(reduce into (map pre-image %)) + scale-extents))) + +(defn valid-scale-measure? + "Checks if the input is a valid scale measure." + [sm] + (let [scale-extents (extents (scale sm)) + pre-image (pre-image-measure sm)] + (every? #(extent? (context sm) + (reduce into (map pre-image %))) + scale-extents))) + + +(defn smeasure? + "Checks if the input is a valid scale measure." + [sm] + (and (instance? ScaleMeasure sm) + (valid-scale-measure? sm))) From c9a849758d1fab6efb27b97bd84ab66c5587e635 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Thu, 16 Apr 2020 09:05:54 +0200 Subject: [PATCH 009/117] Added naive Object Clustering --- src/main/clojure/conexp/fca/smeasure.clj | 30 ++++++++++++++++++++++++ 1 file changed, 30 insertions(+) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 30d08c76c..bd2ba5056 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -99,3 +99,33 @@ b) ((incidence s) [a b])))) identity))) + + +(defn cluster-objects-ex [sm obj] + (let [ctx (context sm) + s (scale sm)] + (make-smeasure-nc (context sm) + (make-context (conj (difference (set (objects s)) obj) + obj) + (attributes s) + (fn [a b] + (if (set? a) + (some #((incidence s) [% b]) + a) + ((incidence s) [a b])))) + (fn [a] (if (get obj a) obj a))))) + +(defn cluster-objects-all [sm obj] + (let [ctx (context sm) + s (scale sm)] + (make-smeasure-nc (context sm) + (make-context (conj (difference (set (objects s)) obj) + obj) + (attributes s) + (fn [a b] + (if (set? a) + (every? #((incidence s) [% b]) + a) + ((incidence s) [a b])))) + (fn [a] (if (get obj a) obj a))))) + From 2fa96e31b43e91d0272ecc5a283452a8be1c28a2 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Mon, 27 Apr 2020 14:10:58 +0200 Subject: [PATCH 010/117] smeasures now with clustering - Made async fast concepts compuatation usable for other methods - Moved transformation algorithms into their own ns - Implemented Cluster Scale Measure Algorithms that compute valid clusterings given an initial set --- src/main/clojure/conexp/base.clj | 1 - .../clojure/conexp/fca/concept_transform.clj | 98 +++++++++ src/main/clojure/conexp/fca/cover.clj | 135 +++++++----- src/main/clojure/conexp/fca/fast.clj | 73 ++++++- src/main/clojure/conexp/fca/pqcores.clj | 66 ------ src/main/clojure/conexp/fca/smeasure.clj | 192 +++++++++++++----- 6 files changed, 394 insertions(+), 171 deletions(-) create mode 100644 src/main/clojure/conexp/fca/concept_transform.clj diff --git a/src/main/clojure/conexp/base.clj b/src/main/clojure/conexp/base.clj index c56dcd24a..15f51b738 100644 --- a/src/main/clojure/conexp/base.clj +++ b/src/main/clojure/conexp/base.clj @@ -764,7 +764,6 @@ metadata (as provided by def) merged into the metadata of the original." [base-set] (map set (comb/subsets (seq base-set)))) - ;;; Next Closure (defn lectic-<_i diff --git a/src/main/clojure/conexp/fca/concept_transform.clj b/src/main/clojure/conexp/fca/concept_transform.clj new file mode 100644 index 000000000..5dd8a1a43 --- /dev/null +++ b/src/main/clojure/conexp/fca/concept_transform.clj @@ -0,0 +1,98 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.concept-transform + (:require [conexp.base :refer :all] + [conexp.fca.contexts :refer :all] + [conexp.fca.cover :refer :all])) + + + +;;; transformer algorithms using the cover structure + +(defn transform-bv-cover + "Transforms the concept lattice of ctx1 to that of ctx2 using the + algorithm presented in 'Knowledge Cores in Large Formal Contexts' + The methods input are the two contexts and the concept lattice of + ctx1 as cover relation generated by cover.clj. For ctx1 and ctx2 it + required that there exists a super context ctx such that ctx1 and + ctx2 are induced subcontexts of ctx. + + This method is useful for larger contexts ctx1 and ctx2 which have + many objects and attributes in common." + [ctx1 ctx2 bv1] + (let [;; update the set of attributes of the ctx and bv first + shared-attributes (intersection (attributes ctx2) (attributes ctx1)) + remove-ctx1-attributes-bv (attribute-deletion-cover bv1 ctx1 (difference (attributes ctx1) shared-attributes)) + ctx2-only-attributes (difference (attributes ctx2) (attributes ctx1)) + attr-intermediate-ctx (make-context (objects ctx1) (attributes ctx2) + (fn [a b] (if (contains? (objects ctx2) a) + ((incidence ctx2) [a b]) + ((incidence ctx1) [a b])))) + insert-ctx2-attributes-bv (attribute-insertion-cover remove-ctx1-attributes-bv attr-intermediate-ctx ctx2-only-attributes) + ;; To update all objects, we update the attributes of the dual + ;; context + dual-bv (dual-concept-cover insert-ctx2-attributes-bv) + shared-objects (intersection (objects ctx1) (objects ctx2)) + dual-ctx (dual-context attr-intermediate-ctx) + remove-ctx1-objects-bv (attribute-deletion-cover + dual-bv (make-context shared-objects (attributes dual-ctx) (incidence dual-ctx)) + (difference (objects ctx1) shared-objects)) + ctx2-only-objects (difference (objects ctx2) (objects ctx1)) + insert-ctx2-objects-bv (attribute-insertion-cover remove-ctx1-objects-bv (dual-context ctx2) ctx2-only-objects)] + (dual-concept-cover insert-ctx2-objects-bv))) + +(defn transform-bv-subctx-cover + "Transforms the concept lattice of ctx1 to that of ctx2 using the + algorithm presented in 'Knowledge Cores in Large Formal Contexts' + The methods input are the two contexts and the concept lattice of + ctx1 as cover relation generated by cover.clj. For ctx1 and ctx2 it + required that ctx2 is a subcontext of ctx1 + + This method is useful for larger contexts ctx1 and ctx2 which have + many objects and attributes in common." + [ctx1 ctx2 bv1] + (let [;; update the set of attributes of the ctx and bv first + shared-attributes (attributes ctx2) + remove-ctx1-attributes-bv (attribute-intersection-cover bv1 shared-attributes) + + ;; To update all objects, we update the attributes of the dual + ;; context + dual-bv (dual-concept-cover remove-ctx1-attributes-bv) + shared-objects (objects ctx2) + remove-ctx1-objects-bv (attribute-intersection-cover dual-bv shared-objects)] + (dual-concept-cover remove-ctx1-objects-bv))) + +(defn transform-bv-intents-cores-cover + "Transforms the intent lattice of ctx1 to that of ctx2 using the + algorithm presented in 'Knowledge Cores in Large Formal Contexts' + The methods input are the two contexts and the concept lattice of + ctx1 as cover relation generated by cover.clj. For ctx1 and ctx2 it + required that ctx2 is a pkcore of ctx1. + + This method is useful for larger contexts ctx1 and ctx2 which have + many objects and attributes in common." + [ctx1 core bv1 p] + (cover-reducer ctx1 core p)) + +;;; general transformer + +(defn transform-bv + "Transforms the set of concepts of ctx1 to that of ctx2 using the + algorithm presented in 'Knowledge Cores in Large Formal Contexts' + The methods input are the two contexts and the set of concepts + ctx1. For ctx1 and ctx2 it required that there exists a super + context ctx such that ctx1 and ctx2 are induced subcontexts of ctx. + + This method is useful for larger contexts ctx1 and ctx2 which have + many objects and attributes in common." + [ctx1 ctx2 concepts1] + (let [bv1 (generate-concept-cover concepts1) + bv2 (dual-concept-cover (transform-bv-cover ctx1 ctx2 bv1))] + (map #(vec [% (get-in bv2 [% :extent])]) (keys bv2)))) + diff --git a/src/main/clojure/conexp/fca/cover.clj b/src/main/clojure/conexp/fca/cover.clj index 410371830..e78d3e450 100644 --- a/src/main/clojure/conexp/fca/cover.clj +++ b/src/main/clojure/conexp/fca/cover.clj @@ -7,21 +7,25 @@ ;; You must not remove this notice, or any other, from this software. (ns conexp.fca.cover - (:require [conexp.base :exclude [next-closed-set]] + (:require [conexp.base :refer :all] + ; :exclude [next-closed-set]] [conexp.fca.contexts :refer :all] [conexp.fca.fast :refer - [next-closed-set to-hashset to-binary-context - bitwise-attribute-derivation forall-in-bitset - bitwise-object-derivation to-binary-matrix + [next-intent-async + ;next-closed-set + to-hashset to-binary-context + ;bitwise-attribute-derivation + ;bitwise-object-derivation + to-binary-matrix bitwise-context-attribute-closure]] - [clojure.core.reducers :as r] - [clojure.set :refer :all]) + [clojure.core.reducers :as r] + [clojure.core.async :refer [! concepts :fin) + (do + (r/>! concepts (to-hashset attr-order bin-next)) + (recur (next-intent-iterator bin-ctx bin-next))))) + concepts)) + ([ctx] + (next-intent-async ctx #{}))) + +(defn next-extent-async +"This method computes all closed sets starting with 'start (inclusive + start) using next-closure. All closed sets are computed asynchron + and are put into the return channel. The used lectic order has + 'start as lowest elements, such that all computed closed sets + contain at least one element of 'start. + (Read closed sets with Date: Tue, 28 Apr 2020 14:15:05 +0200 Subject: [PATCH 011/117] Bugfix and updated tests --- .../clojure/conexp/fca/concept_transform.clj | 2 +- src/main/clojure/conexp/fca/cover.clj | 39 ++++++++++--------- src/test/clojure/conexp/fca/pqcores_test.clj | 13 ------- 3 files changed, 21 insertions(+), 33 deletions(-) diff --git a/src/main/clojure/conexp/fca/concept_transform.clj b/src/main/clojure/conexp/fca/concept_transform.clj index 5dd8a1a43..429bc77c8 100644 --- a/src/main/clojure/conexp/fca/concept_transform.clj +++ b/src/main/clojure/conexp/fca/concept_transform.clj @@ -41,7 +41,7 @@ shared-objects (intersection (objects ctx1) (objects ctx2)) dual-ctx (dual-context attr-intermediate-ctx) remove-ctx1-objects-bv (attribute-deletion-cover - dual-bv (make-context shared-objects (attributes dual-ctx) (incidence dual-ctx)) + dual-bv dual-ctx (difference (objects ctx1) shared-objects)) ctx2-only-objects (difference (objects ctx2) (objects ctx1)) insert-ctx2-objects-bv (attribute-insertion-cover remove-ctx1-objects-bv (dual-context ctx2) ctx2-only-objects)] diff --git a/src/main/clojure/conexp/fca/cover.clj b/src/main/clojure/conexp/fca/cover.clj index e78d3e450..5f357e78e 100644 --- a/src/main/clojure/conexp/fca/cover.clj +++ b/src/main/clojure/conexp/fca/cover.clj @@ -253,11 +253,11 @@ (fn ([a b] ((incidence old-ctx) [a b])) ([[a b]] ((incidence old-ctx) [a b])))) bin-ctx [obj-vec attr-order (count obj-vec) attr-count bin-incidence] - attribute-concepts (for [i del-attributes] - (let [a (BitSet. attr-count)] - (.set a (.indexOf attr-order i)) - (to-hashset attr-order - (bitwise-context-attribute-closure (count obj-vec) (count attr-order) bin-incidence a)))) + attribute-concepts (for [i del-attributes] + (let [a (BitSet. attr-count)] + (.set a (.indexOf attr-order i)) + (to-hashset attr-order + (bitwise-context-attribute-closure (count obj-vec) (count attr-order) bin-incidence a)))) toupdate (find-all-updates attribute-concepts cover)] (loop [cur (first toupdate) other (rest toupdate) newcover {}] (let [updated-newcover (cover-merger newcover (intersecter cur (get cover cur) prev-attributes))] @@ -378,19 +378,20 @@ already included in new-context and are further given by new-attributes." [cover new-ctx new-attributes] - (let [intent-chan (next-intent-async new-ctx new-attributes :exlusive) - prev-attributes (difference + (if (empty? new-attributes) cover + (let [intent-chan (next-intent-async new-ctx new-attributes :exlusive) + prev-attributes (difference (attributes new-ctx) new-attributes) - cur-lattice (agent cover)] - (loop [next-intent ( Date: Tue, 28 Apr 2020 14:33:11 +0200 Subject: [PATCH 012/117] Added documentation --- src/main/clojure/conexp/fca/smeasure.clj | 60 +++++++++++++++++++----- 1 file changed, 48 insertions(+), 12 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 3bbadf6c2..67ed30ab9 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -35,7 +35,7 @@ (measure [this] measure)) (defn- pre-image-measure - "Returns the pre-image map of a scale measures function." + "Returns the pre-image map of a scale measures function sigma." [sm] (let [m (measure sm)] (if (map? m) @@ -46,7 +46,11 @@ [obj ((measure sm) obj)]))] (apply (partial merge-with into) {} (for [[k v] mapified] {v #{k}})))))) -(defn original-extents [sm] + +(defn original-extents + "Returns the pre-image of all extents whichs image is closed in the + scale." + [sm] (let [scale-extents (extents (scale sm)) pre-image (pre-image-measure sm)] (map #(set (reduce into (map pre-image %))) @@ -66,26 +70,38 @@ (and (instance? ScaleMeasure sm) (valid-scale-measure? sm))) -(defn make-smeasure [ctx scale m] +(defn make-smeasure + "Returns a scale-measure object of the input is a valid scale measure." + [ctx scale m] (let [sm (ScaleMeasure. ctx scale m)] (assert (valid-scale-measure? sm) "The Input is no valid Scale Measure") sm)) -(defn make-smeasure-nc [ctx scale m] +(defn make-smeasure-nc + "Generates a scale measure object without checking the validity." + [ctx scale m] (ScaleMeasure. ctx scale m)) -(defn make-id-smeasure [ctx] +(defn make-id-smeasure + "Generates a scale-measure with the identity map and the context as scale." + [ctx] (make-smeasure-nc ctx ctx identity)) -(defn remove-attributes-sm [sm attr] +(defn remove-attributes-sm + "Removes 'attr attributes from the scale." + [sm attr] (let [s (scale sm) new-scale (make-context (objects s) - (disj (attributes s)) + (disj (attributes s) attr) (incidence s))] (make-smeasure-nc (context sm) new-scale (measure sm)))) -(defn cluster-attributes-all [sm attr] +(defn cluster-attributes-all + "Clusters 'attr attributes in the scale context. + For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. + The new incidence is build such that (g, [attr]) if (g,m) for all m in attr." + [sm attr] (let [ctx (context sm) s (scale sm)] (make-smeasure-nc (context sm) @@ -99,14 +115,22 @@ ((incidence s) [a b])))) (measure sm)))) -(defn- valid-cluster [scale original] +(defn- valid-cluster + "This function is a predicate factory for valid scale measure clustering." + [scale original] (let [get-exts (fn [cover] (set (map #(get-in cover [% :extent]) (keys cover)))) ext (get-exts original)] (fn [clustered-scale] (let [ext-new (get-exts (transform-bv-cover scale clustered-scale original))] (subset? ext-new ext))))) -(defn cluster-attributes-ex [sm attr] +(defn cluster-attributes-ex + "Clusters 'attr attributes in the scale context. + For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. + The new incidence is build such that (g, [attr]) if (g,m) for some m + in attr. If the 'attr cluster does not form a valid scale measure, + a sequence of valid supersets of lowest cardinality is returned." + [sm attr] (let [s (scale sm) apply-cluster (fn [at] (make-context (objects s) (conj (difference (attributes s) attr) at) @@ -124,7 +148,13 @@ (recur (inc i)) (map #(into attr %) valids)))))) -(defn cluster-objects-all [sm obj] +(defn cluster-objects-all + "Clusters 'obj objects in the scale context. + For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. + The new incidence is build such that ([obj],m) if (g,m) for all g + in obj. If the 'obj cluster does not form a valid scale measure, + a sequence of valid supersets of lowest cardinality is returned." + [sm obj] (let [s (scale sm) apply-cluster (fn [o] (make-context (conj (difference (objects s) obj) o) (attributes s) @@ -143,7 +173,13 @@ (map #(into obj %) valids)))))) -(defn cluster-objects-ex [sm obj] +(defn cluster-objects-ex + "Clusters 'obj objects in the scale context. + For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. + The new incidence is build such that ([obj],m) if (g,m) for some g + in obj. If the 'obj cluster does not form a valid scale measure, + a sequence of valid supersets of lowest cardinality is returned." + [sm obj] (let [s (scale sm) apply-cluster (fn [o] (make-context (conj (difference (objects s) obj) o) (attributes s) From f560254226c793b21dfd2009d50cbd8df1c6073e Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 28 Apr 2020 15:03:27 +0200 Subject: [PATCH 013/117] added missing test --- .../conexp/fca/concept_transform_test.clj | 25 +++++++++++++++++++ 1 file changed, 25 insertions(+) create mode 100644 src/test/clojure/conexp/fca/concept_transform_test.clj diff --git a/src/test/clojure/conexp/fca/concept_transform_test.clj b/src/test/clojure/conexp/fca/concept_transform_test.clj new file mode 100644 index 000000000..4effab466 --- /dev/null +++ b/src/test/clojure/conexp/fca/concept_transform_test.clj @@ -0,0 +1,25 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.concept-transform-test + (:use conexp.fca.concept-transform conexp.fca.cover) + (:use conexp.fca.contexts) + (:use clojure.test)) + +(deftest test-transform-bv + (let [ctx1 (make-context (range 5) (range 5) <=) + ctx2 (make-context (range 3 7) (range 3 7) <=) + ctx3 (make-context (range 3) (range 5) <=) + ctx4 (make-context (range 7) (range 7) <=) + bv1 (generate-concept-cover (concepts ctx1)) + bv2 (generate-concept-cover (concepts ctx2)) + bv3 (generate-concept-cover (concepts ctx3)) + bv4 (generate-concept-cover (concepts ctx4))] + (is (= (transform-bv-cover ctx1 ctx2 bv1) bv2)) + (is (= (transform-bv-cover ctx1 ctx3 bv1) bv3)) + (is (= (transform-bv-cover ctx1 ctx4 bv1) bv4)))) From 1f611fb877e9b1b8f3f2e60e7f525392089ad8d0 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Wed, 29 Apr 2020 09:27:59 +0200 Subject: [PATCH 014/117] Fixed bug in object clustering --- src/main/clojure/conexp/fca/smeasure.clj | 61 +++++++++++++++++------- 1 file changed, 44 insertions(+), 17 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 67ed30ab9..57738abbc 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -120,9 +120,9 @@ [scale original] (let [get-exts (fn [cover] (set (map #(get-in cover [% :extent]) (keys cover)))) ext (get-exts original)] - (fn [clustered-scale] + (fn [clustered-scale pre-image] (let [ext-new (get-exts (transform-bv-cover scale clustered-scale original))] - (subset? ext-new ext))))) + (subset? (set (map pre-image ext-new)) ext))))) (defn cluster-attributes-ex "Clusters 'attr attributes in the scale context. @@ -133,20 +133,29 @@ [sm attr] (let [s (scale sm) apply-cluster (fn [at] (make-context (objects s) - (conj (difference (attributes s) attr) at) - (fn [a b] - (if (set? b) - (some #((incidence s) [a %]) - b) - ((incidence s) [a b]))))) + (conj (difference (attributes s) at) at) + (fn [a b] + (if (set? b) + (some #((incidence s) [a %]) + b) + ((incidence s) [a b]))))) original (generate-concept-cover (concepts s)) + comp-scale-image identity + scale-pre-image identity valid-cluster? (valid-cluster s original)] - (loop [i 1] + (loop [i 0] (let [candidates (comb/combinations (seq (difference (attributes s) attr)) i) - valids (filter #(valid-cluster? (apply-cluster (into attr %))) candidates)] + valids (filter #(valid-cluster? (apply-cluster (into attr %)) scale-pre-image) candidates)] (if (empty? valids) (recur (inc i)) - (map #(into attr %) valids)))))) + (if (empty? (first valids)) + (let [new-scale (apply-cluster attr)] + (make-smeasure-nc (context sm) + (make-context (objects new-scale) + (attributes new-scale) + (incidence-relation new-scale)) + (comp comp-scale-image (measure sm)))) + (map #(into attr %) valids))))))) (defn cluster-objects-all "Clusters 'obj objects in the scale context. @@ -156,7 +165,7 @@ a sequence of valid supersets of lowest cardinality is returned." [sm obj] (let [s (scale sm) - apply-cluster (fn [o] (make-context (conj (difference (objects s) obj) o) + apply-cluster (fn [o] (make-context (conj (difference (objects s) o) o) (attributes s) (fn [a b] (if (set? a) @@ -164,13 +173,22 @@ a) ((incidence s) [a b]))))) original (generate-concept-cover (concepts s)) + comp-scale-image (fn [g] (if (get obj g) obj g)) + scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) valid-cluster? (valid-cluster s original)] (loop [i 0] (let [candidates (comb/combinations (seq (difference (objects s) obj)) i) - valids (filter #(valid-cluster? (apply-cluster (into obj %))) candidates)] + valids (filter #(valid-cluster? (apply-cluster (into obj %)) (scale-pre-image (into obj %))) candidates)] (if (empty? valids) (recur (inc i)) - (map #(into obj %) valids)))))) + (if (empty? (first valids)) + (let [new-scale (apply-cluster obj)] + (make-smeasure-nc (context sm) + (make-context (objects new-scale) + (attributes new-scale) + (incidence-relation new-scale)) + (comp comp-scale-image (measure sm)))) + (map #(into obj %) valids))))))) (defn cluster-objects-ex @@ -181,7 +199,7 @@ a sequence of valid supersets of lowest cardinality is returned." [sm obj] (let [s (scale sm) - apply-cluster (fn [o] (make-context (conj (difference (objects s) obj) o) + apply-cluster (fn [o] (make-context (conj (difference (objects s) o) o) (attributes s) (fn [a b] (if (set? a) @@ -189,13 +207,22 @@ a) ((incidence s) [a b]))))) original (generate-concept-cover (concepts s)) + comp-scale-image (fn [g] (if (get obj g) obj g)) + scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) valid-cluster? (valid-cluster s original)] (loop [i 0] (let [candidates (comb/combinations (seq (difference (objects s) obj)) i) - valids (filter #(valid-cluster? (apply-cluster (into obj %))) candidates)] + valids (filter #(valid-cluster? (apply-cluster (into obj %)) (scale-pre-image (into obj %))) candidates)] (if (empty? valids) (recur (inc i)) - (map #(into obj %) valids)))))) + (if (empty? (first valids)) + (let [new-scale (apply-cluster obj)] + (make-smeasure-nc (context sm) + (make-context (objects new-scale) + (attributes new-scale) + (incidence-relation new-scale)) + (comp comp-scale-image (measure sm)))) + (map #(into obj %) valids))))))) ;; (defn cluster-attributes-ex [sm attr] ;; (let [ctx (context sm) From f52db81652335b7dceb99ba8b24014426cddf415 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Wed, 29 Apr 2020 14:43:03 +0200 Subject: [PATCH 015/117] Added tests --- src/main/clojure/conexp/fca/smeasure.clj | 26 ++++++++++- src/test/clojure/conexp/fca/smeasure_test.clj | 44 +++++++++++++++++++ 2 files changed, 69 insertions(+), 1 deletion(-) create mode 100644 src/test/clojure/conexp/fca/smeasure_test.clj diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 57738abbc..3df73fa9c 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -92,7 +92,7 @@ [sm attr] (let [s (scale sm) new-scale (make-context (objects s) - (disj (attributes s) attr) + (difference (attributes s) attr) (incidence s))] (make-smeasure-nc (context sm) new-scale (measure sm)))) @@ -224,6 +224,30 @@ (comp comp-scale-image (measure sm)))) (map #(into obj %) valids))))))) +(defn rename-scale-objects + "Renames objects in the scale. Input the renaming as function on the + set of objects or as key value pairs." + ([sm rename-fn] + (make-smeasure-nc (context sm) + (rename-objects (scale sm) rename-fn) + (comp rename-fn (measure sm)))) + ([sm key val & keyvals] + (let [rename-map (apply hash-map key val keyvals) + rename-fn (fn [o] (or (get rename-map o) o))] + (rename-scale-objects sm rename-fn)))) + +(defn rename-scale-attributes + "Renames attribute in the scale. Input the renaming as function on the + set of attributes or as key value pairs." + ([sm rename-fn] + (make-smeasure-nc (context sm) + (rename-attributes (scale sm) rename-fn) + (measure sm))) + ([sm key val & keyvals] + (let [rename-map (apply hash-map key val keyvals) + rename-fn (fn [a] (or (get rename-map a) a))] + (rename-scale-attributes sm rename-fn)))) + ;; (defn cluster-attributes-ex [sm attr] ;; (let [ctx (context sm) ;; s (scale sm)] diff --git a/src/test/clojure/conexp/fca/smeasure_test.clj b/src/test/clojure/conexp/fca/smeasure_test.clj new file mode 100644 index 000000000..b197eb0fb --- /dev/null +++ b/src/test/clojure/conexp/fca/smeasure_test.clj @@ -0,0 +1,44 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.smeasure-test + (:use conexp.fca.contexts conexp.fca.smeasure conexp.base) + (:use clojure.test)) + + +(deftest test-remove-attributes + (let [ctx (rand-context (range 6) 0.5) + sm (make-id-smeasure ctx) + removed (remove-attributes-sm sm #{1 2})] + (is (= (attributes (scale removed)) #{0 3 4 5})) + (is (smeasure? removed)))) + +(deftest test-rename + (let [ctx (rand-context (range 6) 0.5) + sm (make-id-smeasure ctx) + renamed (rename-scale-attributes + (rename-scale-objects sm 1 "test1" 2 "test2") + inc)] + (is (smeasure? renamed)))) + +(deftest test-clusterings + (let [ctx (rand-context (range 5) 0.5) + sm (make-id-smeasure ctx) + candidates (rest(subsets (range 5))) + valid-attr-cl-all (map #(cluster-attributes-all sm %) candidates) + valid-attr-cl-ex (map #(cluster-attributes-ex sm %) candidates) + valid-obj-cl-all (map #(cluster-objects-all sm %) candidates) + valid-obj-cl-ex (map #(cluster-objects-ex sm %) candidates)] + (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-all))) + (is (< (+ 1 (count (attributes ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-all)))) + (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-ex))) + (is (< (+ 1 (count (attributes ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-ex)))) + (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-all))) + (is (< (+ 1 (count (objects ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-all)))) + (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-ex))) + (is (< (+ 1 (count (objects ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-ex)))))) From cb9b5b41a18b1b4aab6e64e7768097f3d6d43b93 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 5 May 2020 11:01:08 +0200 Subject: [PATCH 016/117] Added interactive scale exploration --- src/main/clojure/conexp/fca/smeasure.clj | 252 +++++++++++++----- src/test/clojure/conexp/fca/smeasure_test.clj | 8 +- 2 files changed, 195 insertions(+), 65 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 3df73fa9c..2738b3da8 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -173,7 +173,7 @@ a) ((incidence s) [a b]))))) original (generate-concept-cover (concepts s)) - comp-scale-image (fn [g] (if (get obj g) obj g)) + comp-scale-image (fn [g] (if (contains? obj g) obj g)) scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) valid-cluster? (valid-cluster s original)] (loop [i 0] @@ -207,7 +207,7 @@ a) ((incidence s) [a b]))))) original (generate-concept-cover (concepts s)) - comp-scale-image (fn [g] (if (get obj g) obj g)) + comp-scale-image (fn [g] (if (contains? obj g) obj g)) scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) valid-cluster? (valid-cluster s original)] (loop [i 0] @@ -248,63 +248,193 @@ rename-fn (fn [a] (or (get rename-map a) a))] (rename-scale-attributes sm rename-fn)))) -;; (defn cluster-attributes-ex [sm attr] -;; (let [ctx (context sm) -;; s (scale sm)] -;; (make-smeasure-nc (context sm) -;; (make-context (objects s) -;; (conj (difference (set (attributes s)) attr) -;; attr) -;; (fn [a b] -;; (if (set? b) -;; (some #((incidence s) [a %]) -;; b) -;; ((incidence s) [a b])))) -;; identity))) - - -;; (defn cluster-objects-ex [sm obj] -;; (let [ctx (context sm) -;; s (scale sm)] -;; (make-smeasure-nc (context sm) -;; (make-context (conj (difference (set (objects s)) obj) -;; obj) -;; (attributes s) -;; (fn [a b] -;; (if (set? a) -;; (some #((incidence s) [% b]) -;; a) -;; ((incidence s) [a b])))) -;; (fn [a] (if (get obj a) obj a))))) - -;; (defn cluster-objects-all-nc [sm obj] -;; (let [ctx (context sm) -;; s (scale sm)] -;; (make-smeasure-nc (context sm) -;; (make-context (conj (difference (set (objects s)) obj) -;; obj) -;; (attributes s) -;; (fn [a b] -;; (if (set? a) -;; (every? #((incidence s) [% b]) -;; a) -;; ((incidence s) [a b])))) -;; (fn [a] (if (get obj a) obj a))))) - -;; (defn- build-obj-all-cluster [obj exts] -;; (let [new-cluster (reduce into obj -;; (filter #(and (not (empty? (intersection obj %))) -;; (proper-subset? (intersection obj %) obj)) -;; exts))] -;; (if (= obj new-cluster) -;; obj -;; (build-obj-all-cluster new-cluster exts)))) - -;; (defn cluster-objects-all [sm obj] -;; (let [cluster (build-obj-all-cluster obj (extents (scale sm)))] -;; (println cluster) -;; (assert -;; (not (some #(= (attributes (scale sm)) (object-derivation (scale sm) #{%})) cluster)) -;; "No valid Object Clustering possible.") -;; (cluster-objects-all-nc sm cluster))) + +;;; Declare REPL commands +(defmulti run-repl-command + "Runs a command for the counterexample REPL." + (fn [& args] (first args))) +(alter-meta! #'run-repl-command assoc :private true) + +(defmulti help-repl-command + "Returns the help string of the given command." + (fn [& args] (first args))) +(alter-meta! #'help-repl-command assoc :private true) + +(defn- suitable-repl-commands + "Returns all known repl commands for query, which can be a symbol or + a string." + [query] + (let [str-query (str query)] + (filter #(.startsWith (str %) str-query) + (remove #{:default} (keys (methods run-repl-command)))))) + +(def ^:private abortion-sentinal (Exception. "You should never see this")) + +(defn- eval-command + "Runs the given REPL command query with state, in the case the query uniquely + determines a command. If not, an error message is printed and state is + returned." + [query state] + (if (= query 'abort) + (throw abortion-sentinal) + (let [suitable-methods (suitable-repl-commands query)] + (cond + (second suitable-methods) + (do + (println "Ambigious command, suitable methods are") + (doseq [name suitable-methods] + (println " " name)) + state), + (empty? suitable-methods) + (do + (println "Unknown command") + state) + :else + (try + (run-repl-command (first suitable-methods) state) + (catch Throwable t + (print "Encountered Error: ") + (println t) + state)))))) + +(defmacro- define-repl-fn [name doc & body] + `(do + (defmethod run-repl-command '~name + ~'[_ state] + (let [~'smeasure (:smeasure ~'state) + + ~'scale (scale ~'smeasure)] + ~@body)) + (defmethod help-repl-command '~name + ~'[_] + ~doc))) + +(define-repl-fn done + "Ends the Scale Exploration." + (assoc state :done true)) + +(define-repl-fn clear + "Clears the current state and restarts from scratch." + (assoc state :smeasure (make-id-smeasure (context scale)))) + +(define-repl-fn truncate + "Enter an attribute that should be removed from the scale." + (assoc state :smeasure + (remove-attributes-sm smeasure + (ask (str "Please enter all to be removed attribute spereated by ';': \n") + #(map read-string (clojure.string/split (str (read-line)) #";")) + #(subset? % (attributes scale)) + "The attributes are not all present, please enter an existing attribute: \n")))) + +(define-repl-fn rename + "Renames objects or attributes in the scale." + (let [rename-kind (ask (str "Please enter if you want to rename attributes (:attributes) or objects (:objects): \n") + #(read-string (str (read-line))) + #(or (= :objects %) (= :attributes %)) + "The input must be :attributes or :objects: \n") + rename-method (get {:objects rename-scale-objects :attributes rename-scale-attributes} + rename-kind) + rename-content (ask (str "Please all " (rename-kind {:attributes "attributes" :objects "objects"}) + " that should be renamed and their new name with ; seperator (name1;new-name1;name2;...): \n") + #(map read-string (clojure.string/split (str (read-line)) #";")) + (fn [input] (and (even? (count input)) + (every? + #(contains? ((rename-kind {:attributes attributes :objects objects}) scale) %) + (take-nth 2 input)))) + (str "Input must be ; seperated an contain only " (rename-kind {:attributes "attributes" :objects "objects"}) "of the scale and their new name:\n"))] + (if (empty? rename-content) state + (assoc state :smeasure (apply rename-method smeasure rename-content))))) + +(define-repl-fn cluster + "Apply a clustering to the scales objects or attributes." + (let [cluster-kind (ask (str "Please enter if you want to cluster attributes (:attributes) or objects (:objects): \n") + #(read-string (str (read-line))) + #(or (= :objects %) (= :attributes %)) + "The input must be :attributes or :objects: \n") + cluster-incidence (ask (str "Please enter if their common (:all) or conjoined (:ex) incidence is used as new cluster incidences: \n") + #(read-string (str (read-line))) + #(or (= :all %) (= :ex %)) + "The input must be :all or :ex: \n") + cluster-method (get-in {:objects {:ex cluster-objects-ex :all cluster-objects-all} + :attributes {:ex cluster-attributes-ex :all cluster-attributes-all}} + [cluster-kind cluster-incidence]) + cluster-content (ask (str "Please enter all " (cluster-kind {:attributes "attributes" :objects "objects"}) " to be clustered with ; seperator: \n") + #(set (map read-string (clojure.string/split (str (read-line)) #";"))) + (fn [input] (every? + #(contains? ((cluster-kind {:attributes attributes :objects objects}) scale) %) + input)) + (str "Input must be ; seperated an contain only " (cluster-kind {:attributes "attributes" :objects "objects"}) "of the scale:\n"))] + (if (empty? cluster-content) state + (let [clustered (cluster-method smeasure cluster-content)] + (if (smeasure? clustered) + (assoc state :smeasure clustered) + (let [decision (ask (str "Your input does not form a valid Scale Measure. Here are some valid super-sets of your input with lowest possible cardinality: \n" + (clojure.string/join ", " + (map (partial apply str) + (seq (zipmap + (map #(str "(" % "): ") (range (count clustered))) + clustered))))"\n" + "Enter the number of one of these clusters or -1 for none of them: \n") + #(read-string (str (read-line))) + #(and (<= -1 %) (< % (count clustered))) + (str"The input must a number between -1 and " (count clustered) "\n"))] + (if (= -1 decision) + state + (assoc state :smeasure (cluster-method smeasure (nth clustered decision)))))))))) + +(define-repl-fn show + "Prints the current scale context, attributes or objects." + [state] + (let [toshow (ask (str "Please enter if you want display the scale (:context) its attributes (:attributes) or objects (:objects): \n") + #(read-string (str (read-line))) + #(or (= :objects %) (= :attributes %) (= :context %)) + "The input must be :context, :attributes or :objects: \n")] + (println "\n" ((toshow {:context identity + :attributes (comp (partial clojure.string/join "; ") attributes) + :objects (comp (partial clojure.string/join "; ") objects)}) + scale)) + state)) + +(define-repl-fn help + "Prints help." + (let [commands (suitable-repl-commands "")] + (println "Type «abort» to abort exploration.") + (println "Any other command can be abbreviated, as long as this is unambigious.") + (doseq [cmd commands] + (println (str " " cmd)) + (println (str " -> " (help-repl-command cmd)))) + state)) +;;; Scale Exploration + +(defn scale-exploration + "Exploration for a scale context to measure a given context. + The exploration is done with online editing methods. + + - rename: Rename objects or attributes of the scale + - cluster: Clusters objects or attributes in the scale + The cluster incidence is set as either the common + or conjoined incidences of all entries + - truncate: Removes attributes form the scale + - clear: Restarts the exploration + + general functions for exploration interaction + - show: prints the current scale + - done: finishes exploration + - help: prints doc string" + [ctx] + (assert (context? ctx) "Input must be a Context.") + (println (:doc (meta #'scale-exploration)) "\n\n\n") + (println "Start scale exploration for:\n" ctx) + (loop [state {:smeasure (make-id-smeasure ctx)}] + (let [evaluated (eval-command (ask (str "Please enter an operation:\n") + #(read-string (str (read-line))) + (constantly true) + "Input must be a valid command: \n") state)] + (if (:done evaluated) + (:smeasure evaluated) + (recur evaluated))))) + + +; todo 2D begriffsverband wenn nicht kreuz graph bipartite +; rotes buch diff --git a/src/test/clojure/conexp/fca/smeasure_test.clj b/src/test/clojure/conexp/fca/smeasure_test.clj index b197eb0fb..98b02eb90 100644 --- a/src/test/clojure/conexp/fca/smeasure_test.clj +++ b/src/test/clojure/conexp/fca/smeasure_test.clj @@ -35,10 +35,10 @@ valid-obj-cl-all (map #(cluster-objects-all sm %) candidates) valid-obj-cl-ex (map #(cluster-objects-ex sm %) candidates)] (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-all))) - (is (< (+ 1 (count (attributes ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-all)))) + (is (<= (+ 1 (count (attributes ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-all)))) (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-ex))) - (is (< (+ 1 (count (attributes ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-ex)))) + (is (<= (+ 1 (count (attributes ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-ex)))) (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-all))) - (is (< (+ 1 (count (objects ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-all)))) + (is (<= (+ 1 (count (objects ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-all)))) (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-ex))) - (is (< (+ 1 (count (objects ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-ex)))))) + (is (<= (+ 1 (count (objects ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-ex)))))) From 0fda7a35b293667676c38e8d6cfe7a6b027f364e Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Fri, 8 May 2020 13:18:33 +0200 Subject: [PATCH 017/117] added draft for genetic algorithm --- src/main/clojure/conexp/fca/smeasure.clj | 121 ++++++++++++++++++++++- 1 file changed, 119 insertions(+), 2 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 2738b3da8..cc9fa816a 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -11,7 +11,9 @@ [conexp.fca.contexts :refer :all] [conexp.fca.concept-transform :refer :all] [conexp.fca.cover :refer [generate-concept-cover]] - [clojure.math.combinatorics :as comb])) + [clojure.math.combinatorics :as comb] + [loom.graph :as lg] + [loom.alg :as la])) (defprotocol Smeasure (context [sm] "Returns the original context that is measured.") @@ -437,4 +439,119 @@ ; todo 2D begriffsverband wenn nicht kreuz graph bipartite -; rotes buch +; rotes buch Satz 36 page 134 +; Genau dann ist die Ferrersdimension von (G, M, I) höchstens zwei, wenn der Un- +; verträglichkeitsgraph bipartit ist. + + +(defn cross-graph + "For a formal context (G,M,I) the graph is defined + as (I,E), with (g,m)(h,n) in E, if and only if (g,n) not in I + and (h,m) not in I." + [cxt] + (let [obj (objects cxt) atr (attributes cxt) + vert (filter (incidence cxt) + (reduce concat (for [g obj] (for [m atr] [g m])))) + incidences (zipmap vert (for [v1 vert] + (filter (fn [v2] + (and (not ((incidence cxt) [(first v1) (peek v2)])) + (not (( incidence cxt) [(first v2) (peek v1)])))) + vert)))] + (lg/graph incidences))) + + +;;genetic algorithm + +(defn- two-ferres-covering + "Given a formal context compute a covering of the incidence relation + by two ferres relations." + [ctx] + + ) + +(defn- fill-individual + "Inserts as many objects/ attributes to the context as possible". + [ctx ind] + (let [tofill-obj (difference (objects ctx) (objects ind)) + tofill-attr (difference (attributes ctx) (attributes ind)) + tofill (concept (zip (repeat :attr) tofill-attr) + (zip (repeat :obj) tofill-obj)) + recreate-individual (fn [param] (make-context + (:obj param) (:attr param) + (incidence ctx)))] + (->> tofill + shuffle + (reduce #(if (fit??? %1 %2) ;todo + (update %1 (first %2) conj (second %2)) + %1) + {:attr (attributes ind) + :obj (objects ind)}) + recreate-individual))) + +(defn- breeding + "Given two individuals, i.e. contexts, breeds a next new individual by + first computing the context of common attributes and + objects. Secondly as many attributes/objects of ctx are inserted + without increasing the order dimension of the new individual." + [ctx ind1 ind2] + (->> (make-context + (intersection (objects ind1) (objects ind2)) + (intersection (attributes ind1) (attributes ind2)) + (incidence ctx)) + (fill-individual ctx))) + +(defn- breed-next-generation + "Given the current generation of contexts, breeds the next generation." + [ctx generation] + (let [survivors (->> generation + (sort-by #(* (count (objects %)) + (count (attributes %))))) + [suvivors ]] + + ) + + + ) + +(defn- first-generation + "Computes a first random generation of contexts with order dimension + at most two." + [ctx]) + +(defn- genetic-2d-subctx + "Genetic algorithm to determine a maximal sub-context with order + dimension at most two. Maximal in terms of number of objects times + number of attributes." + [ctx]) + +;; post processing + +(defn- fit-rest + "This method is a helper method for suggest_2d and given a scale + context and an original context, fits as many missing + objects/attributes to the scale by clustering without increasing the order + dimension of the scale concept lattice." + [ctx scale] + ; compute ferres covering + ; loop over attribtues/objects + ) + +;; Suggest Scale + +(defn suggest_2d + "This Method is a genetic algorithm to determine a scale whichs + concept lattice is of order dimension 2D. The methods simulated by + this algorithm are cluster methods only and for comprehensibility we + use only one cluster variation (:all, :or) at a time. Further note + that nested clusters of the same type (:all, :ex) are equivalent to + their flattened correspondence. This method uses a genetic algorithm + that determines a large sub-context, i.e. the number of objects + times attributes, whichs concept lattice is of order dimension at + most two. After that missing attributes are combined with existing + objects, attributes such that they preserve the order dimension." + [ctx] + ; first determine subcontext by genetic algorithm + ; second fill in all missing attributes objects + (-> ctx + genetic-2d-subctx + (fit-rest ctx))) From 4816a7e073bb1b0cc028cb62215e4feeae15abb5 Mon Sep 17 00:00:00 2001 From: De Narm Date: Sat, 9 May 2020 17:06:33 +0200 Subject: [PATCH 018/117] Terminal output --- src/main/clojure/conexp/fca/smeasure.clj | 229 +++++++++++++++-------- 1 file changed, 153 insertions(+), 76 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 3df73fa9c..b56d0eb79 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -7,7 +7,7 @@ ;; You must not remove this notice, or any other, from this software. (ns conexp.fca.smeasure - (:require [conexp.base :refer :all] + (:require [conexp.base :refer :all] [conexp.fca.contexts :refer :all] [conexp.fca.concept-transform :refer :all] [conexp.fca.cover :refer [generate-concept-cover]] @@ -23,7 +23,7 @@ (equals [this other] (and (= (class this) (class other)) (= (.context this) (.context ^ScaleMeasure other)) - (every? #(= ((.measure this) %) + (every? #(= ((.measure this) %) ((.measure ^ScaleMeasure other) %)) (objects context)))) (hashCode [this] @@ -34,20 +34,97 @@ (scale [this] scale) (measure [this] measure)) -(defn- pre-image-measure +;;; visualization terminal + +(defn ^String smeasure-to-string + "Prints smeasures in a human readable form." + [sm] + (let [context (context sm) + scale (scale sm) + mapping (measure sm) + groups (group-by #(mapping %) (objects context)) + ;; + ctx-incident? (incidence context) + sca-incident? (incidence scale) + ;; + max-att-ctx (reduce #(max %1 (count (str %2))) 0 (attributes context)) + max-obj-ctx (reduce #(max %1 (count (str %2))) 0 (objects context)) + max-att-sca (reduce #(max %1 (count (str %2))) 0 (attributes scale)) + max-obj-sca (reduce #(max %1 (count (str %2))) 0 (objects scale)) + ;; + seg-line [(ensure-length "" max-obj-ctx "-") "-+" + (for [att (attributes context)] + (ensure-length "" (inc (count (print-str att))) "-")) + " " + (ensure-length "" max-obj-sca "-") "-+" + (for [att (attributes scale)] + (ensure-length "" (inc (count (print-str att))) "-")) + "\n"]] + (with-str-out + ;; header + (ensure-length "" max-obj-ctx " ") " |" (for [att (attributes context)] + [(print-str att) " "]) + " " + (ensure-length "" max-obj-ctx " ") " |" (for [att (attributes scale)] + [(print-str att) " "]) "\n" + (for [[k group] groups] + ;; first line in group + [seg-line + (ensure-length (print-str (first group)) max-obj-ctx) + " |" + (for [att (attributes context)] + [(ensure-length (if (ctx-incident? [(first group) att]) "x" ".") + (count (print-str att))) + " "]) + " ⟶ " + (ensure-length (print-str (mapping (first group))) max-obj-sca) + " |" + (for [att (attributes scale)] + [(ensure-length (if (sca-incident? [(mapping(first group)) att]) + "x" ".") + (count (print-str att))) + " "]) + "\n" + ;; remaining lines + (for [obj (drop 1 group)] + [(ensure-length (print-str obj) max-obj-ctx) " |" + (for [att (attributes context)] + [(ensure-length (if (ctx-incident? [obj att]) "x" ".") + (count (print-str att))) + " "]) + " " + (ensure-length "" max-obj-ctx " ") " |" + (for [att (attributes scale)] + [(ensure-length "" (count (print-str att)) " ") + " "]) + "\n"])])))) + +(defn print-smeasure + "Prints the result of applying smeasure-to-string to the given + smeasure." + [sm] + (print (apply smeasure-to-string sm))) + +(defmethod print-method ScaleMeasure [sm out] + (.write ^java.io.Writer out + ^String (smeasure-to-string sm))) + +;;; + +(defn- pre-image-measure "Returns the pre-image map of a scale measures function sigma." [sm] (let [m (measure sm)] (if (map? m) - (apply (partial merge-with into) {} + (apply (partial merge-with into) {} (for [[k v] m] {v #{k}})) - (let [mapified (into {} - (for [obj (objects (context sm))] + (let [mapified (into {} + (for [obj (objects (context sm))] [obj ((measure sm) obj)]))] - (apply (partial merge-with into) {} + (apply (partial merge-with into) {} (for [[k v] mapified] {v #{k}})))))) -(defn original-extents +(defn original-extents "Returns the pre-image of all extents whichs image is closed in the scale." [sm] @@ -70,14 +147,14 @@ (and (instance? ScaleMeasure sm) (valid-scale-measure? sm))) -(defn make-smeasure +(defn make-smeasure "Returns a scale-measure object of the input is a valid scale measure." [ctx scale m] (let [sm (ScaleMeasure. ctx scale m)] (assert (valid-scale-measure? sm) "The Input is no valid Scale Measure") sm)) -(defn make-smeasure-nc +(defn make-smeasure-nc "Generates a scale measure object without checking the validity." [ctx scale m] (ScaleMeasure. ctx scale m)) @@ -87,57 +164,57 @@ [ctx] (make-smeasure-nc ctx ctx identity)) -(defn remove-attributes-sm +(defn remove-attributes-sm "Removes 'attr attributes from the scale." [sm attr] (let [s (scale sm) - new-scale (make-context (objects s) + new-scale (make-context (objects s) (difference (attributes s) attr) (incidence s))] (make-smeasure-nc (context sm) new-scale (measure sm)))) -(defn cluster-attributes-all +(defn cluster-attributes-all "Clusters 'attr attributes in the scale context. For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. - The new incidence is build such that (g, [attr]) if (g,m) for all m in attr." + The new incidence is build such that (g, [attr]) if (g,m) for all m in attr." [sm attr] (let [ctx (context sm) s (scale sm)] - (make-smeasure-nc (context sm) - (make-context (objects s) + (make-smeasure-nc (context sm) + (make-context (objects s) (conj (difference (set (attributes s)) attr) - attr) - (fn [a b] - (if (set? b) - (every? #((incidence s) [a %]) - b) - ((incidence s) [a b])))) + attr) + (fn [a b] + (if (set? b) + (every? #((incidence s) [a %]) + b) + ((incidence s) [a b])))) (measure sm)))) -(defn- valid-cluster +(defn- valid-cluster "This function is a predicate factory for valid scale measure clustering." [scale original] (let [get-exts (fn [cover] (set (map #(get-in cover [% :extent]) (keys cover)))) ext (get-exts original)] - (fn [clustered-scale pre-image] + (fn [clustered-scale pre-image] (let [ext-new (get-exts (transform-bv-cover scale clustered-scale original))] (subset? (set (map pre-image ext-new)) ext))))) -(defn cluster-attributes-ex +(defn cluster-attributes-ex "Clusters 'attr attributes in the scale context. For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. The new incidence is build such that (g, [attr]) if (g,m) for some m in attr. If the 'attr cluster does not form a valid scale measure, - a sequence of valid supersets of lowest cardinality is returned." + a sequence of valid supersets of lowest cardinality is returned." [sm attr] (let [s (scale sm) - apply-cluster (fn [at] (make-context (objects s) - (conj (difference (attributes s) at) at) - (fn [a b] - (if (set? b) - (some #((incidence s) [a %]) - b) + apply-cluster (fn [at] (make-context (objects s) + (conj (difference (attributes s) at) at) + (fn [a b] + (if (set? b) + (some #((incidence s) [a %]) + b) ((incidence s) [a b]))))) original (generate-concept-cover (concepts s)) comp-scale-image identity @@ -150,27 +227,27 @@ (recur (inc i)) (if (empty? (first valids)) (let [new-scale (apply-cluster attr)] - (make-smeasure-nc (context sm) + (make-smeasure-nc (context sm) (make-context (objects new-scale) (attributes new-scale) (incidence-relation new-scale)) (comp comp-scale-image (measure sm)))) (map #(into attr %) valids))))))) -(defn cluster-objects-all +(defn cluster-objects-all "Clusters 'obj objects in the scale context. For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. The new incidence is build such that ([obj],m) if (g,m) for all g in obj. If the 'obj cluster does not form a valid scale measure, - a sequence of valid supersets of lowest cardinality is returned." + a sequence of valid supersets of lowest cardinality is returned." [sm obj] (let [s (scale sm) - apply-cluster (fn [o] (make-context (conj (difference (objects s) o) o) + apply-cluster (fn [o] (make-context (conj (difference (objects s) o) o) (attributes s) - (fn [a b] - (if (set? a) - (every? #((incidence s) [% b]) - a) + (fn [a b] + (if (set? a) + (every? #((incidence s) [% b]) + a) ((incidence s) [a b]))))) original (generate-concept-cover (concepts s)) comp-scale-image (fn [g] (if (get obj g) obj g)) @@ -183,7 +260,7 @@ (recur (inc i)) (if (empty? (first valids)) (let [new-scale (apply-cluster obj)] - (make-smeasure-nc (context sm) + (make-smeasure-nc (context sm) (make-context (objects new-scale) (attributes new-scale) (incidence-relation new-scale)) @@ -191,20 +268,20 @@ (map #(into obj %) valids))))))) -(defn cluster-objects-ex +(defn cluster-objects-ex "Clusters 'obj objects in the scale context. For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. The new incidence is build such that ([obj],m) if (g,m) for some g in obj. If the 'obj cluster does not form a valid scale measure, - a sequence of valid supersets of lowest cardinality is returned." + a sequence of valid supersets of lowest cardinality is returned." [sm obj] (let [s (scale sm) - apply-cluster (fn [o] (make-context (conj (difference (objects s) o) o) + apply-cluster (fn [o] (make-context (conj (difference (objects s) o) o) (attributes s) - (fn [a b] - (if (set? a) - (some #((incidence s) [% b]) - a) + (fn [a b] + (if (set? a) + (some #((incidence s) [% b]) + a) ((incidence s) [a b]))))) original (generate-concept-cover (concepts s)) comp-scale-image (fn [g] (if (get obj g) obj g)) @@ -217,7 +294,7 @@ (recur (inc i)) (if (empty? (first valids)) (let [new-scale (apply-cluster obj)] - (make-smeasure-nc (context sm) + (make-smeasure-nc (context sm) (make-context (objects new-scale) (attributes new-scale) (incidence-relation new-scale)) @@ -228,7 +305,7 @@ "Renames objects in the scale. Input the renaming as function on the set of objects or as key value pairs." ([sm rename-fn] - (make-smeasure-nc (context sm) + (make-smeasure-nc (context sm) (rename-objects (scale sm) rename-fn) (comp rename-fn (measure sm)))) ([sm key val & keyvals] @@ -240,7 +317,7 @@ "Renames attribute in the scale. Input the renaming as function on the set of attributes or as key value pairs." ([sm rename-fn] - (make-smeasure-nc (context sm) + (make-smeasure-nc (context sm) (rename-attributes (scale sm) rename-fn) (measure sm))) ([sm key val & keyvals] @@ -251,44 +328,44 @@ ;; (defn cluster-attributes-ex [sm attr] ;; (let [ctx (context sm) ;; s (scale sm)] -;; (make-smeasure-nc (context sm) -;; (make-context (objects s) +;; (make-smeasure-nc (context sm) +;; (make-context (objects s) ;; (conj (difference (set (attributes s)) attr) -;; attr) -;; (fn [a b] -;; (if (set? b) -;; (some #((incidence s) [a %]) -;; b) -;; ((incidence s) [a b])))) +;; attr) +;; (fn [a b] +;; (if (set? b) +;; (some #((incidence s) [a %]) +;; b) +;; ((incidence s) [a b])))) ;; identity))) ;; (defn cluster-objects-ex [sm obj] ;; (let [ctx (context sm) ;; s (scale sm)] -;; (make-smeasure-nc (context sm) +;; (make-smeasure-nc (context sm) ;; (make-context (conj (difference (set (objects s)) obj) -;; obj) -;; (attributes s) -;; (fn [a b] -;; (if (set? a) -;; (some #((incidence s) [% b]) -;; a) -;; ((incidence s) [a b])))) +;; obj) +;; (attributes s) +;; (fn [a b] +;; (if (set? a) +;; (some #((incidence s) [% b]) +;; a) +;; ((incidence s) [a b])))) ;; (fn [a] (if (get obj a) obj a))))) ;; (defn cluster-objects-all-nc [sm obj] ;; (let [ctx (context sm) ;; s (scale sm)] -;; (make-smeasure-nc (context sm) +;; (make-smeasure-nc (context sm) ;; (make-context (conj (difference (set (objects s)) obj) -;; obj) -;; (attributes s) -;; (fn [a b] -;; (if (set? a) -;; (every? #((incidence s) [% b]) -;; a) -;; ((incidence s) [a b])))) +;; obj) +;; (attributes s) +;; (fn [a b] +;; (if (set? a) +;; (every? #((incidence s) [% b]) +;; a) +;; ((incidence s) [a b])))) ;; (fn [a] (if (get obj a) obj a))))) ;; (defn- build-obj-all-cluster [obj exts] @@ -303,7 +380,7 @@ ;; (defn cluster-objects-all [sm obj] ;; (let [cluster (build-obj-all-cluster obj (extents (scale sm)))] ;; (println cluster) -;; (assert +;; (assert ;; (not (some #(= (attributes (scale sm)) (object-derivation (scale sm) #{%})) cluster)) ;; "No valid Object Clustering possible.") ;; (cluster-objects-all-nc sm cluster))) From 141a14490cff91cf9be24dffd3d663940bacd430 Mon Sep 17 00:00:00 2001 From: De Narm Date: Sat, 9 May 2020 17:14:30 +0200 Subject: [PATCH 019/117] Terminal output smeasure --- src/main/clojure/conexp/fca/smeasure.clj | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index b56d0eb79..8feb0479d 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -103,7 +103,7 @@ "Prints the result of applying smeasure-to-string to the given smeasure." [sm] - (print (apply smeasure-to-string sm))) + (print (smeasure-to-string sm))) (defmethod print-method ScaleMeasure [sm out] (.write ^java.io.Writer out From 9f765454ce06e0b7c26b3dc9bb89c139cab12065 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Mon, 11 May 2020 15:59:40 +0200 Subject: [PATCH 020/117] added genetic algorithm --- src/main/clojure/conexp/fca/smeasure.clj | 208 ++++++++++++++++------- 1 file changed, 145 insertions(+), 63 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index cc9fa816a..16dc0dbe7 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -13,7 +13,8 @@ [conexp.fca.cover :refer [generate-concept-cover]] [clojure.math.combinatorics :as comb] [loom.graph :as lg] - [loom.alg :as la])) + [loom.alg :as la]) + (:import [org.dimdraw Bipartite])) (defprotocol Smeasure (context [sm] "Returns the original context that is measured.") @@ -442,87 +443,159 @@ ; rotes buch Satz 36 page 134 ; Genau dann ist die Ferrersdimension von (G, M, I) höchstens zwei, wenn der Un- ; verträglichkeitsgraph bipartit ist. +(defn incompatibility-graph + "For a formal context computes the imcompatibility graph of its + incidence relation." + [ctx] + (let [nodes (difference (cross-product (objects ctx) (attributes ctx)) + (incidence-relation ctx)) + incompatible? (fn [[[g m] [h n]]] + (and ((incidence ctx) [g n]) + ((incidence ctx) [h m]))) + edges (filter incompatible? (cross-product nodes nodes))] + (apply lg/graph edges))) + + +(defmulti addable? + "For a bipartite 'Unverstraeglichkeitsgraph' of a subset of attributes + and objects of a context, computes if adding an object/attribute + preserves the bipartite property." + (fn [& args] (first args))) - -(defn cross-graph - "For a formal context (G,M,I) the graph is defined - as (I,E), with (g,m)(h,n) in E, if and only if (g,n) not in I - and (h,m) not in I." - [cxt] - (let [obj (objects cxt) atr (attributes cxt) - vert (filter (incidence cxt) - (reduce concat (for [g obj] (for [m atr] [g m])))) - incidences (zipmap vert (for [v1 vert] - (filter (fn [v2] - (and (not ((incidence cxt) [(first v1) (peek v2)])) - (not (( incidence cxt) [(first v2) (peek v1)])))) - vert)))] - (lg/graph incidences))) +(defmethod addable? :object + [_ graph subset obj] + (let [obj-nodes (filter #(= obj (first %)) (lg/nodes graph))] + (loop [[cur & other] obj-nodes + added subset] + (if (nil? cur) added + (if (la/bipartite? (lg/subgraph graph (conj subset cur))) + ;(not (. Bipartite isInOddCycle (:adj graph) added cur)) + (recur other (conj added cur)) + false))))) + +(defmethod addable? :attribute + [_ graph subset attr] + (let [attr-nodes (filter #(= attr (second %)) (lg/nodes graph))] + (loop [[cur & other] attr-nodes + added subset] + (if (nil? cur) added + (if (not (. Bipartite isInOddCycle (:adj graph) added cur)) + (recur other (conj added cur)) + false))))) + + +(defn fill-individual + "Inserts as many objects/attributes to the individual as possible. + An individual is a set of nodes of the contexts incompatibility graph." + [ctx graph ind] + (let [;; missing objects and attributes in the individual + tofill-obj (difference (objects ctx) (into #{} (map first ind))) + tofill-attr (difference (attributes ctx) (into #{} (map second ind))) + tofill (into [] (concat (zip (repeat :attribute) tofill-attr) + (zip (repeat :object) tofill-obj))) + ;; add if addable + add-if-addable (fn [tmp-ind [kind toadd]] + (let [added (addable? kind graph tmp-ind toadd)] + (if added added tmp-ind)))] + (->> tofill + shuffle + (reduce add-if-addable ind)))) ;;genetic algorithm -(defn- two-ferres-covering - "Given a formal context compute a covering of the incidence relation - by two ferres relations." - [ctx] - - ) - -(defn- fill-individual - "Inserts as many objects/ attributes to the context as possible". - [ctx ind] - (let [tofill-obj (difference (objects ctx) (objects ind)) - tofill-attr (difference (attributes ctx) (attributes ind)) - tofill (concept (zip (repeat :attr) tofill-attr) - (zip (repeat :obj) tofill-obj)) - recreate-individual (fn [param] (make-context - (:obj param) (:attr param) - (incidence ctx)))] - (->> tofill - shuffle - (reduce #(if (fit??? %1 %2) ;todo - (update %1 (first %2) conj (second %2)) - %1) - {:attr (attributes ind) - :obj (objects ind)}) - recreate-individual))) +(def- generation-size 10) +(def- generations 7) +(def- survival-ratio 0.3) +(def- mutation-rate 0) + +(def- survival-count (int (* generation-size survival-ratio))) + +(defn- fitness + "Computes the fitness of an individual." + [ind] + (let [distinct-obj (->> ind + (map first) + set count) + distinct-attr (->> ind + (map second) + set count)] + (* distinct-attr + distinct-obj))) + +(defn- mutation + "Mutates the current individual by removing an object or attribute + given a probability." + [ctx graph ind] + (let [ind-obj (map first ind) + ind-attr (map second ind) + mutated-obj (random-sample (- 1 mutation-rate) ind-obj) + mutated-attr (random-sample (- 1 mutation-rate) ind-attr)] + (into #{} (filter #(and (some #{(first %)} mutated-obj) + (some #{(second %)} mutated-attr)) ind)))) (defn- breeding "Given two individuals, i.e. contexts, breeds a next new individual by first computing the context of common attributes and objects. Secondly as many attributes/objects of ctx are inserted without increasing the order dimension of the new individual." - [ctx ind1 ind2] - (->> (make-context - (intersection (objects ind1) (objects ind2)) - (intersection (attributes ind1) (attributes ind2)) - (incidence ctx)) - (fill-individual ctx))) - -(defn- breed-next-generation - "Given the current generation of contexts, breeds the next generation." - [ctx generation] - (let [survivors (->> generation - (sort-by #(* (count (objects %)) - (count (attributes %))))) - [suvivors ]] - - ) - + [ctx graph ind1 ind2] + (->> (intersection ind1 ind2) + ;(mutation ctx graph) + (fill-individual ctx graph))) - ) +(defn- next-generation + "Given the current generation of contexts, breeds the next generation." + [ctx graph generation] + (let [fitness (->> generation + (sort-by fitness) + (take survival-count)) + survivals (take survival-count fitness) + pairing (->> survivals + shuffle + (partition 2)) + rand-pair (fn [] (->> survivals + shuffle + (take 2)))] + (into [] + (concat survivals + (->> (concat pairing (repeat (rand-pair))) + (take (- generation-size survival-count)) + (into []) + (map #(apply breeding ctx graph %))))))) (defn- first-generation "Computes a first random generation of contexts with order dimension at most two." - [ctx]) - -(defn- genetic-2d-subctx + [ctx graph] + (into [] + (for [_ (range generation-size)] + (fill-individual ctx graph #{})))) + +(defn fitness + "Returns the fitness of an individual." + [ind] + (* (count (set (map first ind))) ; number of distinct objects + (count (set (map second ind))))) ; number of distinct attributes + +(defn genetic-2d-subctx "Genetic algorithm to determine a maximal sub-context with order dimension at most two. Maximal in terms of number of objects times number of attributes." - [ctx]) + [ctx] + (let [graph (incompatibility-graph ctx) + ind2subctx (fn [ind] + (make-context + (set (map first ind)) + (set (map second ind)) + (incidence ctx)))] + (loop [n generations + generation (first-generation ctx graph)] + (if (= n 0) + (->> generation + (apply max-key fitness) + ind2subctx) + (recur (dec n) (next-generation ctx graph generation)))))) ;; post processing @@ -532,6 +605,7 @@ objects/attributes to the scale by clustering without increasing the order dimension of the scale concept lattice." [ctx scale] + scale ; compute ferres covering ; loop over attribtues/objects ) @@ -555,3 +629,11 @@ (-> ctx genetic-2d-subctx (fit-rest ctx))) + + +;; (defn- two-ferres-covering +;; "Given a formal context compute a covering of the incidence relation +;; by two ferres relations." +;; [ctx] + +;; ) From 64a009b55fc7daeaa37713c5f4acbe23eca52178 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 12 May 2020 16:33:38 +0200 Subject: [PATCH 021/117] genetic 2d subctx --- src/main/clojure/conexp/fca/smeasure.clj | 235 ++++++++++++++--------- 1 file changed, 148 insertions(+), 87 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 16dc0dbe7..041805e8f 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -456,47 +456,81 @@ (apply lg/graph edges))) -(defmulti addable? - "For a bipartite 'Unverstraeglichkeitsgraph' of a subset of attributes +(defmulti add-if-bipartite + "For a bipartite incompatibility graph of a subset of attributes and objects of a context, computes if adding an object/attribute preserves the bipartite property." (fn [& args] (first args))) -(defmethod addable? :object - [_ graph subset obj] - (let [obj-nodes (filter #(= obj (first %)) (lg/nodes graph))] - (loop [[cur & other] obj-nodes - added subset] - (if (nil? cur) added - (if (la/bipartite? (lg/subgraph graph (conj subset cur))) - ;(not (. Bipartite isInOddCycle (:adj graph) added cur)) - (recur other (conj added cur)) - false))))) - -(defmethod addable? :attribute - [_ graph subset attr] - (let [attr-nodes (filter #(= attr (second %)) (lg/nodes graph))] - (loop [[cur & other] attr-nodes - added subset] - (if (nil? cur) added - (if (not (. Bipartite isInOddCycle (:adj graph) added cur)) - (recur other (conj added cur)) - false))))) +(defmethod add-if-bipartite :object + [_ graph {iobjs :objects iattr :attributes :as ind} add-objs] + (let [old-nodes (into #{} + (filter #(and (contains? iattr (second %)) + (contains? iobjs (first %))) (lg/nodes graph))) + {new-objs :objects :as new-ind} (update ind :objects conj add-objs) + new-nodes (into #{} + (filter #(and (contains? new-objs (first %)) + (contains? iattr (second %))) (lg/nodes graph))) + ;; A node can be added if it is not in an odd cycle with itself + not-addable? (fn [n] + (. Bipartite isInOddCycle (:adj graph) (disj new-nodes n) n))] + (if (->> (difference new-nodes old-nodes) + (some not-addable?)) + ind new-ind))) + +(defmethod add-if-bipartite :attribute + [_ graph {iobjs :objects iattr :attributes :as ind} add-attr] + (let [old-nodes (into #{} + (filter #(and (contains? iattr (second %)) + (contains? iobjs (first %))) (lg/nodes graph))) + {new-attr :attributes :as new-ind} (update ind :attributes conj add-attr) + new-nodes (into #{} + (filter #(and (contains? new-attr (second %)) + (contains? iobjs (first %))) (lg/nodes graph))) + ;; A node can be added if it is not in an odd cycle with itself + not-addable? (fn [n] + (. Bipartite isInOddCycle (:adj graph) (disj new-nodes n) n))] + (if (->> (difference new-nodes old-nodes) + (some not-addable?)) + ind new-ind))) + + +;; (defmethod add-if-bipartite :object +;; [_ graph {iobjs :objects iattr :attributes :as ind} add-objs] +;; (let [;; old-nodes (filter #(and (contains? iattr (second %)) +;; ;; (contains? iobjs (first %))) (lg/nodes graph)) +;; {new-objs :objects :as new-ind} (update ind :objects conj add-objs) +;; new-nodes (filter #(and (contains? iattr (second %)) +;; (contains? new-objs (first %))) (lg/nodes graph))] +;; (if (la/bipartite? (lg/subgraph graph new-nodes)) +;; new-ind +;; ind))) + + +;; (defmethod add-if-bipartite :attribute +;; [_ graph {iobjs :objects iattr :attributes :as ind} add-attr] +;; (let [;; old-nodes (filter #(and (contains? iattr (second %)) +;; ;; (contains iobjs (first %))) (lg/nodes graph)) +;; {new-attr :attributes :as new-ind} (update ind :attributes conj add-attr) +;; new-nodes (filter #(and (contains? iobjs (first %)) +;; (contains? new-attr (second %))) (lg/nodes graph))] +;; (if (la/bipartite? (lg/subgraph graph new-nodes)) +;; new-ind +;; ind))) (defn fill-individual "Inserts as many objects/attributes to the individual as possible. An individual is a set of nodes of the contexts incompatibility graph." - [ctx graph ind] + [ctx graph {iobjs :objects iattr :attributes :as ind}] (let [;; missing objects and attributes in the individual - tofill-obj (difference (objects ctx) (into #{} (map first ind))) - tofill-attr (difference (attributes ctx) (into #{} (map second ind))) + tofill-obj (difference (objects ctx) iobjs) + tofill-attr (difference (attributes ctx) iattr) tofill (into [] (concat (zip (repeat :attribute) tofill-attr) (zip (repeat :object) tofill-obj))) ;; add if addable add-if-addable (fn [tmp-ind [kind toadd]] - (let [added (addable? kind graph tmp-ind toadd)] - (if added added tmp-ind)))] + (add-if-bipartite kind graph tmp-ind toadd))] (->> tofill shuffle (reduce add-if-addable ind)))) @@ -504,98 +538,125 @@ ;;genetic algorithm -(def- generation-size 10) -(def- generations 7) -(def- survival-ratio 0.3) -(def- mutation-rate 0) - -(def- survival-count (int (* generation-size survival-ratio))) - -(defn- fitness - "Computes the fitness of an individual." - [ind] - (let [distinct-obj (->> ind - (map first) - set count) - distinct-attr (->> ind - (map second) - set count)] - (* distinct-attr - distinct-obj))) +(defn- make-args-map + "Returns default args updated by user input." + [args] + (let [default-args {:generation-size 30 :generations 30 + :survival-ratio 0.1 :mutation-rate 0.3 + :fresh-chance 0.05 + :init {:objects #{} :attributes #{}}}] + (assert (and (:init args) + (not (la/bipartite? (incompatibility-graph (:init args))))) + "Inputted initial Context must have a concept lattice of + order dimension two.") + (-> (reduce #(assoc %1 %2 (%2 args)) default-args (keys args)) + (assoc :survival-count (int (* generation-size survival-ratio))) + (update :init #(if (context? %) + {:objects (objects %) :attributes (attributes %)} + %))))) + +(defmulti fitness + "For a bipartite incompatibility graph of a subset of attributes + and objects of a context, computes if adding an object/attribute + preserves the bipartite property." + (fn [& args] (:mode (first args)))) + +(defmethod fitness :concepts + [_ ctx {iobjs :objects iattr :attributes :as ind}] + (-> (make-context iobjs iattr (incidence ctx)) + concepts + count)) + +(defmethod fitness :ctx-nontrivia + [_ ctx {iobjs :objects iattr :attributes :as ind}] + (let [sub-ctx (make-context iobjs iattr (incidence ctx)) + nontrivia-obj (filter #(not (empty? (object-derivation sub-ctx #{%}))) + (objects sub-ctx)) + nontrivia-attr (filter #(not (empty? (attribute-derivation sub-ctx #{%}))) + (attributes sub-ctx))] + (* (count nontrivia-obj) + (count nontrivia-attr)))) + +(defmethod fitness :incidence + [_ ctx {iobjs :objects iattr :attributes :as ind}] + (let [sub-ctx (make-context iobjs iattr (incidence ctx))] + (count (incidence-relation sub-ctx)))) + +(defmethod fitness :default + [_ ctx {iobjs :objects iattr :attributes :as ind}] + (* (count iobjs) + (count iattr))) (defn- mutation "Mutates the current individual by removing an object or attribute given a probability." - [ctx graph ind] - (let [ind-obj (map first ind) - ind-attr (map second ind) - mutated-obj (random-sample (- 1 mutation-rate) ind-obj) - mutated-attr (random-sample (- 1 mutation-rate) ind-attr)] - (into #{} (filter #(and (some #{(first %)} mutated-obj) - (some #{(second %)} mutated-attr)) ind)))) + [args ctx graph {iobjs :objects iattr :attributes :as ind}] + (if (> fresh-chance (rand)) + (fill-individual ctx graph (:init args)) + (let [mutated-obj (into #{} (random-sample (- 1 (:mutation-rate args)) iobjs)) + mutated-attr (into #{} (random-sample (- 1 (:mutation-rate args)) iattr))] + (-> ind + (assoc :objects mutated-obj) + (assoc :attributes mutated-attr))))) (defn- breeding "Given two individuals, i.e. contexts, breeds a next new individual by first computing the context of common attributes and objects. Secondly as many attributes/objects of ctx are inserted without increasing the order dimension of the new individual." - [ctx graph ind1 ind2] - (->> (intersection ind1 ind2) - ;(mutation ctx graph) + [args ctx graph + {iobjs :objects iattr :attributes} {iobjs2 :objects iattr2 :attributes}] + (->> {:objects (intersection iobjs iobjs2) :attributes (intersection iattr iattr2)} + (mutation args ctx graph) (fill-individual ctx graph))) (defn- next-generation "Given the current generation of contexts, breeds the next generation." - [ctx graph generation] - (let [fitness (->> generation - (sort-by fitness) - (take survival-count)) - survivals (take survival-count fitness) + [args ctx graph generation] + (let [fitness-vals (->> generation + (sort-by (partial fitness args ctx)) + (take (:survival-count args))) + survivals (take (:survival-count args) fitness-vals) pairing (->> survivals - shuffle - (partition 2)) + shuffle + (partition 2)) rand-pair (fn [] (->> survivals - shuffle - (take 2)))] + shuffle + (take 2)))] (into [] (concat survivals (->> (concat pairing (repeat (rand-pair))) - (take (- generation-size survival-count)) - (into []) - (map #(apply breeding ctx graph %))))))) + (take (- generation-size survival-count)) + (into []) + (map #(apply breeding args ctx graph %))))))) (defn- first-generation "Computes a first random generation of contexts with order dimension at most two." - [ctx graph] + [args ctx graph] (into [] - (for [_ (range generation-size)] - (fill-individual ctx graph #{})))) + (for [_ (range (:generation-size args))] + (fill-individual ctx graph + (:init args))))) -(defn fitness - "Returns the fitness of an individual." - [ind] - (* (count (set (map first ind))) ; number of distinct objects - (count (set (map second ind))))) ; number of distinct attributes (defn genetic-2d-subctx "Genetic algorithm to determine a maximal sub-context with order dimension at most two. Maximal in terms of number of objects times number of attributes." - [ctx] - (let [graph (incompatibility-graph ctx) - ind2subctx (fn [ind] - (make-context - (set (map first ind)) - (set (map second ind)) - (incidence ctx)))] - (loop [n generations - generation (first-generation ctx graph)] + [ctx & [args]] + (let [args (make-args-map args) + graph (incompatibility-graph ctx) + ind2subctx (fn [{iobjs :objects iattr :attributes}] + (make-context iobjs iattr (incidence ctx)))] + (loop [n (:generations args) + generation (first-generation args ctx graph)] (if (= n 0) (->> generation - (apply max-key fitness) - ind2subctx) - (recur (dec n) (next-generation ctx graph generation)))))) + (apply max-key (partial fitness args ctx)) + ;ind2subctx + ) + (recur (dec n) (next-generation args ctx graph generation)))))) ;; post processing From 57dd8f6f64bf7f2336c75510784db5c8a445e58f Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 12 May 2020 16:50:20 +0200 Subject: [PATCH 022/117] removed debug --- src/main/clojure/conexp/fca/smeasure.clj | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 041805e8f..38f30a211 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -654,8 +654,7 @@ (if (= n 0) (->> generation (apply max-key (partial fitness args ctx)) - ;ind2subctx - ) + ind2subctx) (recur (dec n) (next-generation args ctx graph generation)))))) ;; post processing From ef32ff7b0c6170a0722db078cd6b586d22189d3f Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Wed, 13 May 2020 12:43:04 +0200 Subject: [PATCH 023/117] refectoring --- src/main/clojure/conexp/fca/smeasure.clj | 673 ++++++++++++----------- 1 file changed, 342 insertions(+), 331 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 38f30a211..349013424 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -99,25 +99,6 @@ (incidence s))] (make-smeasure-nc (context sm) new-scale (measure sm)))) - -(defn cluster-attributes-all - "Clusters 'attr attributes in the scale context. - For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. - The new incidence is build such that (g, [attr]) if (g,m) for all m in attr." - [sm attr] - (let [ctx (context sm) - s (scale sm)] - (make-smeasure-nc (context sm) - (make-context (objects s) - (conj (difference (set (attributes s)) attr) - attr) - (fn [a b] - (if (set? b) - (every? #((incidence s) [a %]) - b) - ((incidence s) [a b])))) - (measure sm)))) - (defn- valid-cluster "This function is a predicate factory for valid scale measure clustering." [scale original] @@ -127,121 +108,152 @@ (let [ext-new (get-exts (transform-bv-cover scale clustered-scale original))] (subset? (set (map pre-image ext-new)) ext))))) -(defn cluster-attributes-ex - "Clusters 'attr attributes in the scale context. - For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. - The new incidence is build such that (g, [attr]) if (g,m) for some m - in attr. If the 'attr cluster does not form a valid scale measure, - a sequence of valid supersets of lowest cardinality is returned." - [sm attr] - (let [s (scale sm) - apply-cluster (fn [at] (make-context (objects s) - (conj (difference (attributes s) at) at) +(defmulti cluster-applier + "Clusters attributes or objects in the scale context. + For example the set #{1 2 3} become #{[1 2] 3} in the scale. The + new incidence is build such that (g, [1 2]) if (g,m) for all/some m + in [1 2] in the case of attributes. Possible clusters are + attribute/object clusters with existential and all quantified + incidence." + (fn [type quantifier & args] [type quantifier])) + +(defmethod cluster-applier [:attributes :ex] + [_ _ ctx] + (fn [attr] (make-context (objects ctx) + (conj (difference (attributes ctx) attr) attr) + (fn [a b] + (if (set? b) + (some #((incidence ctx) [a %]) + b) + ((incidence ctx) [a b])))))) + +(defmethod cluster-applier [:attributes :ex] + [_ _ ctx] + (fn [attr] + (make-context (objects ctx) + (conj (difference (set (attributes ctx)) attr) + attr) + (fn [a b] + (if (set? b) + (every? #((incidence ctx) [a %]) + b) + ((incidence ctx) [a b])))))) + +(defmethod cluster-applier [:objects :all] + [_ _ ctx] + (fn [obj] (make-context (conj (difference (objects ctx) obj) obj) + (attributes ctx) (fn [a b] - (if (set? b) - (some #((incidence s) [a %]) - b) - ((incidence s) [a b]))))) - original (generate-concept-cover (concepts s)) - comp-scale-image identity - scale-pre-image identity - valid-cluster? (valid-cluster s original)] - (loop [i 0] - (let [candidates (comb/combinations (seq (difference (attributes s) attr)) i) - valids (filter #(valid-cluster? (apply-cluster (into attr %)) scale-pre-image) candidates)] - (if (empty? valids) - (recur (inc i)) - (if (empty? (first valids)) - (let [new-scale (apply-cluster attr)] - (make-smeasure-nc (context sm) - (make-context (objects new-scale) - (attributes new-scale) - (incidence-relation new-scale)) - (comp comp-scale-image (measure sm)))) - (map #(into attr %) valids))))))) - -(defn cluster-objects-all - "Clusters 'obj objects in the scale context. - For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. - The new incidence is build such that ([obj],m) if (g,m) for all g - in obj. If the 'obj cluster does not form a valid scale measure, - a sequence of valid supersets of lowest cardinality is returned." - [sm obj] - (let [s (scale sm) - apply-cluster (fn [o] (make-context (conj (difference (objects s) o) o) - (attributes s) + (if (set? a) + (every? #((incidence ctx) [% b]) + a) + ((incidence ctx) [a b])))))) +(defmethod cluster-applier [:objects :ex] + [_ _ ctx] + (fn [obj] (make-context (conj (difference (objects ctx) obj) obj) + (attributes ctx) (fn [a b] (if (set? a) - (every? #((incidence s) [% b]) + (some #((incidence ctx) [% b]) a) - ((incidence s) [a b]))))) - original (generate-concept-cover (concepts s)) - comp-scale-image (fn [g] (if (contains? obj g) obj g)) - scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) - valid-cluster? (valid-cluster s original)] - (loop [i 0] - (let [candidates (comb/combinations (seq (difference (objects s) obj)) i) - valids (filter #(valid-cluster? (apply-cluster (into obj %)) (scale-pre-image (into obj %))) candidates)] + ((incidence ctx) [a b])))))) + +(defn- cluster-until-valid + "This is a helper method, that applies a certain clustering until a + valid scale measure is outputted. If not unique, returns a seq of + valid candidates." + [sm init-cluster apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image] + (loop [i 0] + (let [candidates (build-candidates i); (comb/combinations (seq (difference (objects s) obj)) i) + valids (filter valid-cluster? ;#(valid-cluster? (apply-cluster (into obj %)) (scale-pre-image (into obj %))) + candidates)] (if (empty? valids) (recur (inc i)) (if (empty? (first valids)) - (let [new-scale (apply-cluster obj)] + (let [new-scale (apply-cluster init-cluster)] (make-smeasure-nc (context sm) (make-context (objects new-scale) (attributes new-scale) (incidence-relation new-scale)) (comp comp-scale-image (measure sm)))) - (map #(into obj %) valids))))))) + (map #(into init-cluster %) valids)))))) + +(defmulti cluster + "Clusters attributes or objects in the scale context. + For example the set #{1 2 3} become #{[1 2] 3} in the scale. The + new incidence is build such that (g, [1 2]) if (g,m) for all/some m + in [1 2] in the case of attributes. Possible clusters are + attribute/object clusters with existential and all quantified + incidence." + (fn [type quantifier & args] [type quantifier])) + +(defmethod cluster [:attributes :all] + [_ _ sm attr] + (let [ctx (context sm) + s (scale sm) + apply-cluster (cluster-applier :attributes :all s)] + (make-smeasure-nc (context sm) (apply-cluster attr) (measure sm)))) +(defmethod cluster [:attributes :ex] + [_ _ sm attr] + (let [s (scale sm) + apply-cluster (cluster-applier :attributes :ex s) + original (generate-concept-cover (concepts s)) + comp-scale-image identity + scale-pre-image identity + valid-cluster? (valid-cluster s original) + + valid-cluster? (fn [additional-attr] ((valid-cluster s original) + (apply-cluster (into attr additional-attr)) + (scale-pre-image (into attr additional-attr)))) + build-candidates (fn [i] (comb/combinations (seq (difference (attributes s) attr)) i))] + (cluster-until-valid + sm attr apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))) -(defn cluster-objects-ex - "Clusters 'obj objects in the scale context. - For example the attributes #{1 2 3} become #{[1 2] 3} in the scale. - The new incidence is build such that ([obj],m) if (g,m) for some g - in obj. If the 'obj cluster does not form a valid scale measure, - a sequence of valid supersets of lowest cardinality is returned." - [sm obj] +(defmethod cluster [:objects :all] + [_ _ sm obj] (let [s (scale sm) - apply-cluster (fn [o] (make-context (conj (difference (objects s) o) o) - (attributes s) - (fn [a b] - (if (set? a) - (some #((incidence s) [% b]) - a) - ((incidence s) [a b]))))) + apply-cluster (cluster-applier :objects :all s) original (generate-concept-cover (concepts s)) comp-scale-image (fn [g] (if (contains? obj g) obj g)) scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) - valid-cluster? (valid-cluster s original)] - (loop [i 0] - (let [candidates (comb/combinations (seq (difference (objects s) obj)) i) - valids (filter #(valid-cluster? (apply-cluster (into obj %)) (scale-pre-image (into obj %))) candidates)] - (if (empty? valids) - (recur (inc i)) - (if (empty? (first valids)) - (let [new-scale (apply-cluster obj)] - (make-smeasure-nc (context sm) - (make-context (objects new-scale) - (attributes new-scale) - (incidence-relation new-scale)) - (comp comp-scale-image (measure sm)))) - (map #(into obj %) valids))))))) - -(defn rename-scale-objects - "Renames objects in the scale. Input the renaming as function on the + valid-cluster? (fn [additional-obj] ((valid-cluster s original) + (apply-cluster (into obj additional-obj)) + (scale-pre-image (into obj additional-obj)))) + build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] + (cluster-until-valid + sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))) + +(defmethod cluster [:objects :ex] + [_ _ sm obj] + (let [s (scale sm) + apply-cluster (cluster-applier :objects :ex s) + original (generate-concept-cover (concepts s)) + comp-scale-image (fn [g] (if (contains? obj g) obj g)) + scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) + valid-cluster? (fn [additional-obj] ((valid-cluster s original) + (apply-cluster (into obj additional-obj)) + (scale-pre-image (into obj additional-obj)))) + build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] + (cluster-until-valid + sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))) + +(defmulti rename-scale + "Renames objects or attributes in the scale. Input the renaming as function on the set of objects or as key value pairs." - ([sm rename-fn] + (fn [type & args] type)) + +(defmethod rename-scale :objects + ([_ sm rename-fn] (make-smeasure-nc (context sm) (rename-objects (scale sm) rename-fn) (comp rename-fn (measure sm)))) - ([sm key val & keyvals] + ([_ sm key val & keyvals] (let [rename-map (apply hash-map key val keyvals) rename-fn (fn [o] (or (get rename-map o) o))] - (rename-scale-objects sm rename-fn)))) - -(defn rename-scale-attributes - "Renames attribute in the scale. Input the renaming as function on the - set of attributes or as key value pairs." + (rename-scale :objects sm rename-fn)))) + +(defmethod rename-scale :attributes ([sm rename-fn] (make-smeasure-nc (context sm) (rename-attributes (scale sm) rename-fn) @@ -249,194 +261,7 @@ ([sm key val & keyvals] (let [rename-map (apply hash-map key val keyvals) rename-fn (fn [a] (or (get rename-map a) a))] - (rename-scale-attributes sm rename-fn)))) - - - -;;; Declare REPL commands -(defmulti run-repl-command - "Runs a command for the counterexample REPL." - (fn [& args] (first args))) -(alter-meta! #'run-repl-command assoc :private true) - -(defmulti help-repl-command - "Returns the help string of the given command." - (fn [& args] (first args))) -(alter-meta! #'help-repl-command assoc :private true) - -(defn- suitable-repl-commands - "Returns all known repl commands for query, which can be a symbol or - a string." - [query] - (let [str-query (str query)] - (filter #(.startsWith (str %) str-query) - (remove #{:default} (keys (methods run-repl-command)))))) - -(def ^:private abortion-sentinal (Exception. "You should never see this")) - -(defn- eval-command - "Runs the given REPL command query with state, in the case the query uniquely - determines a command. If not, an error message is printed and state is - returned." - [query state] - (if (= query 'abort) - (throw abortion-sentinal) - (let [suitable-methods (suitable-repl-commands query)] - (cond - (second suitable-methods) - (do - (println "Ambigious command, suitable methods are") - (doseq [name suitable-methods] - (println " " name)) - state), - (empty? suitable-methods) - (do - (println "Unknown command") - state) - :else - (try - (run-repl-command (first suitable-methods) state) - (catch Throwable t - (print "Encountered Error: ") - (println t) - state)))))) - -(defmacro- define-repl-fn [name doc & body] - `(do - (defmethod run-repl-command '~name - ~'[_ state] - (let [~'smeasure (:smeasure ~'state) - - ~'scale (scale ~'smeasure)] - ~@body)) - (defmethod help-repl-command '~name - ~'[_] - ~doc))) - -(define-repl-fn done - "Ends the Scale Exploration." - (assoc state :done true)) - -(define-repl-fn clear - "Clears the current state and restarts from scratch." - (assoc state :smeasure (make-id-smeasure (context scale)))) - -(define-repl-fn truncate - "Enter an attribute that should be removed from the scale." - (assoc state :smeasure - (remove-attributes-sm smeasure - (ask (str "Please enter all to be removed attribute spereated by ';': \n") - #(map read-string (clojure.string/split (str (read-line)) #";")) - #(subset? % (attributes scale)) - "The attributes are not all present, please enter an existing attribute: \n")))) - -(define-repl-fn rename - "Renames objects or attributes in the scale." - (let [rename-kind (ask (str "Please enter if you want to rename attributes (:attributes) or objects (:objects): \n") - #(read-string (str (read-line))) - #(or (= :objects %) (= :attributes %)) - "The input must be :attributes or :objects: \n") - rename-method (get {:objects rename-scale-objects :attributes rename-scale-attributes} - rename-kind) - rename-content (ask (str "Please all " (rename-kind {:attributes "attributes" :objects "objects"}) - " that should be renamed and their new name with ; seperator (name1;new-name1;name2;...): \n") - #(map read-string (clojure.string/split (str (read-line)) #";")) - (fn [input] (and (even? (count input)) - (every? - #(contains? ((rename-kind {:attributes attributes :objects objects}) scale) %) - (take-nth 2 input)))) - (str "Input must be ; seperated an contain only " (rename-kind {:attributes "attributes" :objects "objects"}) "of the scale and their new name:\n"))] - (if (empty? rename-content) state - (assoc state :smeasure (apply rename-method smeasure rename-content))))) - -(define-repl-fn cluster - "Apply a clustering to the scales objects or attributes." - (let [cluster-kind (ask (str "Please enter if you want to cluster attributes (:attributes) or objects (:objects): \n") - #(read-string (str (read-line))) - #(or (= :objects %) (= :attributes %)) - "The input must be :attributes or :objects: \n") - cluster-incidence (ask (str "Please enter if their common (:all) or conjoined (:ex) incidence is used as new cluster incidences: \n") - #(read-string (str (read-line))) - #(or (= :all %) (= :ex %)) - "The input must be :all or :ex: \n") - cluster-method (get-in {:objects {:ex cluster-objects-ex :all cluster-objects-all} - :attributes {:ex cluster-attributes-ex :all cluster-attributes-all}} - [cluster-kind cluster-incidence]) - cluster-content (ask (str "Please enter all " (cluster-kind {:attributes "attributes" :objects "objects"}) " to be clustered with ; seperator: \n") - #(set (map read-string (clojure.string/split (str (read-line)) #";"))) - (fn [input] (every? - #(contains? ((cluster-kind {:attributes attributes :objects objects}) scale) %) - input)) - (str "Input must be ; seperated an contain only " (cluster-kind {:attributes "attributes" :objects "objects"}) "of the scale:\n"))] - (if (empty? cluster-content) state - (let [clustered (cluster-method smeasure cluster-content)] - (if (smeasure? clustered) - (assoc state :smeasure clustered) - (let [decision (ask (str "Your input does not form a valid Scale Measure. Here are some valid super-sets of your input with lowest possible cardinality: \n" - (clojure.string/join ", " - (map (partial apply str) - (seq (zipmap - (map #(str "(" % "): ") (range (count clustered))) - clustered))))"\n" - "Enter the number of one of these clusters or -1 for none of them: \n") - #(read-string (str (read-line))) - #(and (<= -1 %) (< % (count clustered))) - (str"The input must a number between -1 and " (count clustered) "\n"))] - (if (= -1 decision) - state - (assoc state :smeasure (cluster-method smeasure (nth clustered decision)))))))))) - -(define-repl-fn show - "Prints the current scale context, attributes or objects." - [state] - (let [toshow (ask (str "Please enter if you want display the scale (:context) its attributes (:attributes) or objects (:objects): \n") - #(read-string (str (read-line))) - #(or (= :objects %) (= :attributes %) (= :context %)) - "The input must be :context, :attributes or :objects: \n")] - (println "\n" ((toshow {:context identity - :attributes (comp (partial clojure.string/join "; ") attributes) - :objects (comp (partial clojure.string/join "; ") objects)}) - scale)) - state)) - -(define-repl-fn help - "Prints help." - (let [commands (suitable-repl-commands "")] - (println "Type «abort» to abort exploration.") - (println "Any other command can be abbreviated, as long as this is unambigious.") - (doseq [cmd commands] - (println (str " " cmd)) - (println (str " -> " (help-repl-command cmd)))) - state)) -;;; Scale Exploration - -(defn scale-exploration - "Exploration for a scale context to measure a given context. - The exploration is done with online editing methods. - - - rename: Rename objects or attributes of the scale - - cluster: Clusters objects or attributes in the scale - The cluster incidence is set as either the common - or conjoined incidences of all entries - - truncate: Removes attributes form the scale - - clear: Restarts the exploration - - general functions for exploration interaction - - show: prints the current scale - - done: finishes exploration - - help: prints doc string" - [ctx] - (assert (context? ctx) "Input must be a Context.") - (println (:doc (meta #'scale-exploration)) "\n\n\n") - (println "Start scale exploration for:\n" ctx) - (loop [state {:smeasure (make-id-smeasure ctx)}] - (let [evaluated (eval-command (ask (str "Please enter an operation:\n") - #(read-string (str (read-line))) - (constantly true) - "Input must be a valid command: \n") state)] - (if (:done evaluated) - (:smeasure evaluated) - (recur evaluated))))) + (rename-scale :attributes sm rename-fn)))) ; todo 2D begriffsverband wenn nicht kreuz graph bipartite @@ -494,32 +319,7 @@ (some not-addable?)) ind new-ind))) - -;; (defmethod add-if-bipartite :object -;; [_ graph {iobjs :objects iattr :attributes :as ind} add-objs] -;; (let [;; old-nodes (filter #(and (contains? iattr (second %)) -;; ;; (contains? iobjs (first %))) (lg/nodes graph)) -;; {new-objs :objects :as new-ind} (update ind :objects conj add-objs) -;; new-nodes (filter #(and (contains? iattr (second %)) -;; (contains? new-objs (first %))) (lg/nodes graph))] -;; (if (la/bipartite? (lg/subgraph graph new-nodes)) -;; new-ind -;; ind))) - - -;; (defmethod add-if-bipartite :attribute -;; [_ graph {iobjs :objects iattr :attributes :as ind} add-attr] -;; (let [;; old-nodes (filter #(and (contains? iattr (second %)) -;; ;; (contains iobjs (first %))) (lg/nodes graph)) -;; {new-attr :attributes :as new-ind} (update ind :attributes conj add-attr) -;; new-nodes (filter #(and (contains? iobjs (first %)) -;; (contains? new-attr (second %))) (lg/nodes graph))] -;; (if (la/bipartite? (lg/subgraph graph new-nodes)) -;; new-ind -;; ind))) - - -(defn fill-individual +(defn- fill-individual "Inserts as many objects/attributes to the individual as possible. An individual is a set of nodes of the contexts incompatibility graph." [ctx graph {iobjs :objects iattr :attributes :as ind}] @@ -535,6 +335,19 @@ shuffle (reduce add-if-addable ind)))) +;; (defn- ind2ctx +;; [] +;; ) + +;; (defn- fill-individual-cluster +;; "Inserts as many objects/attributes to the individual as possible. +;; An individual is a set of nodes of the contexts incompatibility graph." +;; [args ctx {iobjs :objects iattr :attributes :as init-ind}] +;; (let [ind-ctx]) +;; (loop [ind init-ind] + +;; ) +;; ) ;;genetic algorithm @@ -549,11 +362,13 @@ (not (la/bipartite? (incompatibility-graph (:init args))))) "Inputted initial Context must have a concept lattice of order dimension two.") - (-> (reduce #(assoc %1 %2 (%2 args)) default-args (keys args)) - (assoc :survival-count (int (* generation-size survival-ratio))) - (update :init #(if (context? %) - {:objects (objects %) :attributes (attributes %)} - %))))) + (let [combined-args + (-> (reduce #(assoc %1 %2 (%2 args)) default-args (keys args)) + (update :init #(if (context? %) + {:objects (objects %) :attributes (attributes %)} + %)))] + (assoc :survival-count (int (* (:generation-size combined-args) + (:survival-ratio combined-args))))))) (defmulti fitness "For a bipartite incompatibility graph of a subset of attributes @@ -591,7 +406,7 @@ "Mutates the current individual by removing an object or attribute given a probability." [args ctx graph {iobjs :objects iattr :attributes :as ind}] - (if (> fresh-chance (rand)) + (if (> (:fresh-chance args) (rand)) (fill-individual ctx graph (:init args)) (let [mutated-obj (into #{} (random-sample (- 1 (:mutation-rate args)) iobjs)) mutated-attr (into #{} (random-sample (- 1 (:mutation-rate args)) iattr))] @@ -626,7 +441,7 @@ (into [] (concat survivals (->> (concat pairing (repeat (rand-pair))) - (take (- generation-size survival-count)) + (take (- (:generation-size args) (:survival-count args))) (into []) (map #(apply breeding args ctx graph %))))))) @@ -697,3 +512,199 @@ ;; [ctx] ;; ) + +;;; Declare REPL commands +(defmulti run-repl-command + "Runs a command for the counterexample REPL." + (fn [& args] (first args))) +(alter-meta! #'run-repl-command assoc :private true) + +(defmulti help-repl-command + "Returns the help string of the given command." + (fn [& args] (first args))) +(alter-meta! #'help-repl-command assoc :private true) + +(defn- suitable-repl-commands + "Returns all known repl commands for query, which can be a symbol or + a string." + [query] + (let [str-query (str query)] + (filter #(.startsWith (str %) str-query) + (remove #{:default} (keys (methods run-repl-command)))))) + +(def ^:private abortion-sentinal (Exception. "You should never see this")) + +(defn- eval-command + "Runs the given REPL command query with state, in the case the query uniquely + determines a command. If not, an error message is printed and state is + returned." + [query state] + (if (= query 'abort) + (throw abortion-sentinal) + (let [suitable-methods (suitable-repl-commands query)] + (cond + (second suitable-methods) + (do + (println "Ambigious command, suitable methods are") + (doseq [name suitable-methods] + (println " " name)) + state), + (empty? suitable-methods) + (do + (println "Unknown command") + state) + :else + (try + (run-repl-command (first suitable-methods) state) + (catch Throwable t + (print "Encountered Error: ") + (println t) + state)))))) + +(defmacro- define-repl-fn [name doc & body] + `(do + (defmethod run-repl-command '~name + ~'[_ state] + (let [~'smeasure (:smeasure ~'state) + + ~'scale (scale ~'smeasure)] + ~@body)) + (defmethod help-repl-command '~name + ~'[_] + ~doc))) + +(define-repl-fn done + "Ends the Scale Exploration." + (assoc state :done true)) + +(define-repl-fn clear + "Clears the current state and restarts from scratch." + (assoc state :smeasure (make-id-smeasure (context scale)))) + +(define-repl-fn truncate + "Enter an attribute that should be removed from the scale." + (assoc state :smeasure + (remove-attributes-sm smeasure + (ask (str "Please enter all to be removed attribute spereated by ';': \n") + #(map read-string (clojure.string/split (str (read-line)) #";")) + #(subset? % (attributes scale)) + "The attributes are not all present, please enter an existing attribute: \n")))) + +(define-repl-fn rename + "Renames objects or attributes in the scale." + (let [rename-kind (ask (str "Please enter if you want to rename attributes (:attributes) or objects (:objects): \n") + #(read-string (str (read-line))) + #(or (= :objects %) (= :attributes %)) + "The input must be :attributes or :objects: \n") + rename-method (partial rename rename-kind) + rename-content (ask (str "Please all " (rename-kind {:attributes "attributes" :objects "objects"}) + " that should be renamed and their new name with ; seperator (name1;new-name1;name2;...): \n") + #(map read-string (clojure.string/split (str (read-line)) #";")) + (fn [input] (and (even? (count input)) + (every? + #(contains? ((rename-kind {:attributes attributes :objects objects}) scale) %) + (take-nth 2 input)))) + (str "Input must be ; seperated an contain only " (rename-kind {:attributes "attributes" :objects "objects"}) "of the scale and their new name:\n"))] + (if (empty? rename-content) state + (assoc state :smeasure (apply rename-method smeasure rename-content))))) + +(define-repl-fn cluster + "Apply a clustering to the scales objects or attributes." + (let [cluster-kind (ask (str "Please enter if you want to cluster attributes (:attributes) or objects (:objects): \n") + #(read-string (str (read-line))) + #(or (= :objects %) (= :attributes %)) + "The input must be :attributes or :objects: \n") + cluster-incidence (ask (str "Please enter if their common (:all) or conjoined (:ex) incidence is used as new cluster incidences: \n") + #(read-string (str (read-line))) + #(or (= :all %) (= :ex %)) + "The input must be :all or :ex: \n") + cluster-method (partial cluster [cluster-kind cluster-incidence]) + cluster-content (ask (str "Please enter all " (cluster-kind {:attributes "attributes" :objects "objects"}) " to be clustered with ; seperator: \n") + #(set (map read-string (clojure.string/split (str (read-line)) #";"))) + (fn [input] (every? + #(contains? ((cluster-kind {:attributes attributes :objects objects}) scale) %) + input)) + (str "Input must be ; seperated an contain only " (cluster-kind {:attributes "attributes" :objects "objects"}) "of the scale:\n"))] + (if (empty? cluster-content) state + (let [clustered (cluster-method smeasure cluster-content)] + (if (smeasure? clustered) + (assoc state :smeasure clustered) + (let [decision (ask (str "Your input does not form a valid Scale Measure. Here are some valid super-sets of your input with lowest possible cardinality: \n" + (clojure.string/join ", " + (map (partial apply str) + (seq (zipmap + (map #(str "(" % "): ") (range (count clustered))) + clustered))))"\n" + "Enter the number of one of these clusters or -1 for none of them: \n") + #(read-string (str (read-line))) + #(and (<= -1 %) (< % (count clustered))) + (str"The input must a number between -1 and " (count clustered) "\n"))] + (if (= -1 decision) + state + (assoc state :smeasure (cluster-method smeasure (nth clustered decision)))))))))) + +(define-repl-fn show + "Prints the current scale context, attributes or objects." + [state] + (let [toshow (ask (str "Please enter if you want display the scale (:context) its attributes (:attributes) or objects (:objects): \n") + #(read-string (str (read-line))) + #(or (= :objects %) (= :attributes %) (= :context %)) + "The input must be :context, :attributes or :objects: \n")] + (println "\n" ((toshow {:context identity + :attributes (comp (partial clojure.string/join "; ") attributes) + :objects (comp (partial clojure.string/join "; ") objects)}) + scale)) + state)) + +(define-repl-fn help + "Prints help." + (let [commands (suitable-repl-commands "")] + (println "Type «abort» to abort exploration.") + (println "Any other command can be abbreviated, as long as this is unambigious.") + (doseq [cmd commands] + (println (str " " cmd)) + (println (str " -> " (help-repl-command cmd)))) + state)) + +(define-repl-fn suggest + "Suggests a scale with two dimensional concept lattice." + (let [suggestion (suggest_2d (context smeasure))] + (println suggestion) + (if (= 1 (ask "Do you wish to continue with the suggested scale? 1: yes, 0: no:" + #(read-string (str (read-line))) + (constantly true) + "")) + (assoc state :smeasure (make-smeasure-nc (context smeasure) suggestion)) + state))) + +;;; Scale Exploration + +(defn scale-exploration + "Exploration for a scale context to measure a given context. + The exploration is done with online editing methods. + + - rename: Rename objects or attributes of the scale + - cluster: Clusters objects or attributes in the scale + The cluster incidence is set as either the common + or conjoined incidences of all entries + - truncate: Removes attributes form the scale + - clear: Restarts the exploration + + general functions for exploration interaction + - show: prints the current scale + - done: finishes exploration + - help: prints doc string" + [ctx] + (assert (context? ctx) "Input must be a Context.") + (println (:doc (meta #'scale-exploration)) "\n\n\n") + (println "Start scale exploration for:\n" ctx) + (loop [state {:smeasure (make-id-smeasure ctx)}] + (let [evaluated (eval-command (ask (str "Please enter an operation:\n") + #(read-string (str (read-line))) + (constantly true) + "Input must be a valid command: \n") state)] + (if (:done evaluated) + (:smeasure evaluated) + (recur evaluated))))) + + From fc3625d018a2717f21d36237505f0313a65f6c85 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Wed, 13 May 2020 17:26:39 +0200 Subject: [PATCH 024/117] repair cluster method --- src/main/clojure/conexp/fca/smeasure.clj | 97 +++++++++++++++++++----- 1 file changed, 80 insertions(+), 17 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 349013424..e317dd8d1 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -110,12 +110,13 @@ (defmulti cluster-applier "Clusters attributes or objects in the scale context. - For example the set #{1 2 3} become #{[1 2] 3} in the scale. The + For exaegawegaewrgaewrgsfagfagewgwegwegwegmple the set #{1 2 3} become #{[1 2] 3} in the scale. The new incidence is build such that (g, [1 2]) if (g,m) for all/some m in [1 2] in the case of attributes. Possible clusters are attribute/object clusters with existential and all quantified incidence." (fn [type quantifier & args] [type quantifier])) +(alter-meta! #'cluster-applier assoc :private true) (defmethod cluster-applier [:attributes :ex] [_ _ ctx] @@ -164,8 +165,8 @@ valid candidates." [sm init-cluster apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image] (loop [i 0] - (let [candidates (build-candidates i); (comb/combinations (seq (difference (objects s) obj)) i) - valids (filter valid-cluster? ;#(valid-cluster? (apply-cluster (into obj %)) (scale-pre-image (into obj %))) + (let [candidates (build-candidates i) + valids (filter valid-cluster? candidates)] (if (empty? valids) (recur (inc i)) @@ -186,6 +187,7 @@ attribute/object clusters with existential and all quantified incidence." (fn [type quantifier & args] [type quantifier])) +(alter-meta! #'cluster assoc :private true) (defmethod cluster [:attributes :all] [_ _ sm attr] @@ -238,10 +240,42 @@ (cluster-until-valid sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))) + +(defmulti repair-cluster + "Given a scale context constructs a valid smeasure scale by using as + few cluster methods as possible. 'quantifier specifies the cluster + quantifier used by the clustering methods." + (fn [quantifier & args] quantifier)) +(alter-meta! #'repair-cluster assoc :private true) + +(defmethod repair-cluster :all + [_ ctx broken-scale] + (let [br-exts (map #(hash-map :new ((comp first object-concept) %) :obj %) (objects broken-scale)) ; TODO sufficient? all attributes are valid for :all + pre-images (sort-by count + (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat + br-exts)) + not-closed? (fn [e] (let [orig-e (context-object-closure ctx (:new e))] + (if (= orig-e e) false (assoc e :original orig-e)))) + image (fn [o] (some + #(if (contains? % o) % false) (objects broken-scale))) + broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality + (if broken + (let [apply-flattened-cluster (fn [cl] (-> cl + (cluster-applier :objects :all s) + (rename-objects (fn [o] + (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) + #{} o))))) + missing (map image (difference (:original broken) (:new broken))) + tocluster (conj (reduce conj #{} missing) (:obj broken))] + (repair-cluster :all ctx (apply-flattened-cluster broken-scale tocluster))) + broken-scale))) + + (defmulti rename-scale "Renames objects or attributes in the scale. Input the renaming as function on the set of objects or as key value pairs." (fn [type & args] type)) +(alter-meta! #'rename-scale assoc :private true) (defmethod rename-scale :objects ([_ sm rename-fn] @@ -268,7 +302,7 @@ ; rotes buch Satz 36 page 134 ; Genau dann ist die Ferrersdimension von (G, M, I) höchstens zwei, wenn der Un- ; verträglichkeitsgraph bipartit ist. -(defn incompatibility-graph +(defn- incompatibility-graph "For a formal context computes the imcompatibility graph of its incidence relation." [ctx] @@ -286,6 +320,7 @@ and objects of a context, computes if adding an object/attribute preserves the bipartite property." (fn [& args] (first args))) +(alter-meta! #'add-if-bipartite assoc :private true) (defmethod add-if-bipartite :object [_ graph {iobjs :objects iattr :attributes :as ind} add-objs] @@ -335,19 +370,7 @@ shuffle (reduce add-if-addable ind)))) -;; (defn- ind2ctx -;; [] -;; ) -;; (defn- fill-individual-cluster -;; "Inserts as many objects/attributes to the individual as possible. -;; An individual is a set of nodes of the contexts incompatibility graph." -;; [args ctx {iobjs :objects iattr :attributes :as init-ind}] -;; (let [ind-ctx]) -;; (loop [ind init-ind] - -;; ) -;; ) ;;genetic algorithm @@ -375,6 +398,7 @@ and objects of a context, computes if adding an object/attribute preserves the bipartite property." (fn [& args] (:mode (first args)))) +(alter-meta! #'fitness assoc :private true) (defmethod fitness :concepts [_ ctx {iobjs :objects iattr :attributes :as ind}] @@ -618,7 +642,7 @@ #(read-string (str (read-line))) #(or (= :all %) (= :ex %)) "The input must be :all or :ex: \n") - cluster-method (partial cluster [cluster-kind cluster-incidence]) + cluster-method (partial cluster cluster-kind cluster-incidence) cluster-content (ask (str "Please enter all " (cluster-kind {:attributes "attributes" :objects "objects"}) " to be clustered with ; seperator: \n") #(set (map read-string (clojure.string/split (str (read-line)) #";"))) (fn [input] (every? @@ -708,3 +732,42 @@ (recur evaluated))))) +;; (defn- cluster-ind-intersecter +;; "This method computed the intersection between two cluster individuals by computing the splittance." +;; [{iobjs1 :objects iattr1 :attributes :as ind1} +;; {iobjs2 :objects iattr2 :attributes :as ind2}] +;; {:objects (->> iobjs2 +;; ;; computes splitance +;; (reduce (fn [tmp-ind cl] (union (map #(difference % cl) tmp-ind) +;; (map #(intersection % cl) tmp-ind))) +;; iobjs1) +;; ;; remove empty fragment +;; #(disj % #{})) +;; :attributes (->> iattr2 +;; ;; computes splitance +;; (reduce (fn [tmp-ind cl] (union (map #(difference % cl) tmp-ind) +;; (map #(intersection % cl) tmp-ind))) +;; iattr1) +;; ;; remove empty fragment +;; #(disj % #{}))}) + +;; ;; first gen needs to convert each attribute/objects into a set +;; (defn- ind2clustered-ctx +;; "This is a helper method to apply the by the individual specified clustering." +;; [args ctx {iobjs :objects iattr :attributes :as ind}] +;; (let [apply-cluster-obj (fn [tocluster-ctx cl] ((cluster-applier :objects (:obj-cl-quantifier args) tocluster-ctx) cl)) +;; apply-cluster-attr (fn [tocluster-ctx cl] ((cluster-applier :attributes (:attr-cl-quantifier args) tocluster-ctx) cl))] +;; (-> ctx +;; #(reduce apply-cluster-attr % iattr) +;; #(reduce apply-cluster-obj % iobjj)))) + +;; (defn- fill-individual-cluster +;; "Inserts as many objects/attributes to the individual as possible. +;; An individual is a set of nodes of the contexts incompatibility graph." +;; [args ctx {iobjs :objects iattr :attributes :as init-ind}] +;; (let [apply-cluster-obj (fn [tocluster-ctx cl] (if (coll? cl) ((cluster-applier :objects (:obj-cl-quantifier args) tocluster-ctx) cl) tocluster-ctx)) +;; apply-cluster-attr (fn [tocluster-ctx cl] (if (coll? cl) ((cluster-applier :attributes (:attr-cl-quantifier args) tocluster-ctx) cl) tocluster-ctx))] +;; (loop [ind (ind2clustered-ctx args ctx init-ind)] +;; ;; cluster until valid and 2D +;; )) +;; ) From d297f4b18b6fd786730c30d381447a0d1fcfa091 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Wed, 13 May 2020 18:47:40 +0200 Subject: [PATCH 025/117] prepared helper methods for genetic clustering --- src/main/clojure/conexp/fca/smeasure.clj | 148 ++++++++++++++++------- 1 file changed, 104 insertions(+), 44 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index e317dd8d1..db2c59abc 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -158,6 +158,17 @@ (some #((incidence ctx) [% b]) a) ((incidence ctx) [a b])))))) +(defn- flattened-cluster-applier + "Returns a cluster method depending on the 'kind and 'quant specifier." + [ctx kind quant] + (fn [cl] (-> cl + (cluster-applier kind quant ctx) + (rename-objects (fn [o] + (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) + #{} o))) + (rename-attributes (fn [a] + (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) + #{} a)))))) (defn- cluster-until-valid "This is a helper method, that applies a certain clustering until a @@ -240,6 +251,16 @@ (cluster-until-valid sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))) +(defn- flattened-cluster + "This is a wrapper method to flatten the cluster result." + [kind quant sm thing] + (let [result (cluster kind quant sm thing)] + (if (coll? result) + (map (partial reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) #{}) + result) + (rename kind (fn [k] + (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) + #{} k)))))) (defmulti repair-cluster "Given a scale context constructs a valid smeasure scale by using as @@ -260,16 +281,16 @@ #(if (contains? % o) % false) (objects broken-scale))) broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality (if broken - (let [apply-flattened-cluster (fn [cl] (-> cl - (cluster-applier :objects :all s) - (rename-objects (fn [o] - (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) - #{} o))))) + (let [apply-flattened-cluster (flattened-cluster-applier :objects :all broken-scale) missing (map image (difference (:original broken) (:new broken))) tocluster (conj (reduce conj #{} missing) (:obj broken))] (repair-cluster :all ctx (apply-flattened-cluster broken-scale tocluster))) broken-scale))) +;; (defmethod repair-cluster :ex +;; [_ ctx broken-scale] +;; TODO) + (defmulti rename-scale "Renames objects or attributes in the scale. Input the renaming as function on the @@ -354,6 +375,79 @@ (some not-addable?)) ind new-ind))) +(defn- cluster-ind-intersecter + "This method computed the intersection between two cluster individuals by computing the splittance." + [{iobjs1 :objects iattr1 :attributes :as ind1} + {iobjs2 :objects iattr2 :attributes :as ind2}] + {:objects (->> iobjs2 + ;; computes splitance + (reduce (fn [tmp-ind cl] (union (map #(difference % cl) tmp-ind) + (map #(intersection % cl) tmp-ind))) + iobjs1) + ;; remove empty fragment + #(disj % #{})) + :attributes (->> iattr2 + ;; computes splitance + (reduce (fn [tmp-ind cl] (union (map #(difference % cl) tmp-ind) + (map #(intersection % cl) tmp-ind))) + iattr1) + ;; remove empty fragment + #(disj % #{}))}) + +;; first gen needs to convert each attribute/objects into a set +(defn- ind2clustered-ctx + "This is a helper method to apply the by the individual specified clustering." + [args ctx {iobjs :objects iattr :attributes :as ind}] + (let [apply-cluster-obj (fn [tocluster-ctx cl] ((cluster-applier :objects (:obj-cl-quantifier args) tocluster-ctx) cl)) + apply-cluster-attr (fn [tocluster-ctx cl] ((cluster-applier :attributes (:attr-cl-quantifier args) tocluster-ctx) cl))] + (-> ctx + #(reduce apply-cluster-attr % iattr) + #(reduce apply-cluster-obj % iobjj)))) + +(defn- apply-small-rand-cluster + "This is a helper method to apply the smallest clustering out of a few + random valid clusterings." + [args scale] + (let [candidates (if (rand-nth [true false]) + (zip (repeat :object) + (take 3 (partition 2 (shuffle (objects ctx))))) + (zip (repeat :attribute) + (take 3 (partition 2 (shuffle (attributes ctx)))))) + ;; how large the clusters become + key-fkt (fn [[kind thing]] + (let [result (flattened-cluster kind (:quantifier args) + (make-smeasure-nc (:ctx args) scale + (fn [o] + (some #(if (contains? % o) % false) + (objects broken-scale)))) + thing)] + (if (coll? result) (count (first)) + (apply + (map count thing))))) + smallest (min-key key-fkt candidates) + ] + (-> (flattened-cluster (first smallest) (:quantifier args) + (make-smeasure-nc (:ctx args) scale + (fn [o] + (some + #(if (contains? % o) % false) + (objects broken-scale)))) + (second smallest))))) + +(defn- fill-individual-cluster + "Inserts as many objects/attributes to the individual as possible. + An individual is a set of nodes of the contexts incompatibility graph." + [args ctx {iobjs :objects iattr :attributes :as ind}] + (let [repaired-ind (->> ind + (ind2clustered-ctx args ctx) + (repair-cluster :all)) + make-ind-map #(hash-map :objects (objects %) :attributes (attributes %)) + 2dcontext? (comp la/bipartite? incompatibility-graph) + apply-rand-cluster (fn [c] (flattened-cluster-applier :objects :all c))] + (loop [tmp-ind repaired-ind] ;; apply small clusters until 2D + (if (2dcontext? tmp-ind) + (make-ind-map tmp-ind) + (recur (apply-small-rand-cluster args)))))) + (defn- fill-individual "Inserts as many objects/attributes to the individual as possible. An individual is a set of nodes of the contexts incompatibility graph." @@ -372,6 +466,7 @@ + ;;genetic algorithm (defn- make-args-map @@ -400,6 +495,10 @@ (fn [& args] (:mode (first args)))) (alter-meta! #'fitness assoc :private true) +(defmethod fitness :clustered + [& args] + (apply fitness args)) + (defmethod fitness :concepts [_ ctx {iobjs :objects iattr :attributes :as ind}] (-> (make-context iobjs iattr (incidence ctx)) @@ -732,42 +831,3 @@ (recur evaluated))))) -;; (defn- cluster-ind-intersecter -;; "This method computed the intersection between two cluster individuals by computing the splittance." -;; [{iobjs1 :objects iattr1 :attributes :as ind1} -;; {iobjs2 :objects iattr2 :attributes :as ind2}] -;; {:objects (->> iobjs2 -;; ;; computes splitance -;; (reduce (fn [tmp-ind cl] (union (map #(difference % cl) tmp-ind) -;; (map #(intersection % cl) tmp-ind))) -;; iobjs1) -;; ;; remove empty fragment -;; #(disj % #{})) -;; :attributes (->> iattr2 -;; ;; computes splitance -;; (reduce (fn [tmp-ind cl] (union (map #(difference % cl) tmp-ind) -;; (map #(intersection % cl) tmp-ind))) -;; iattr1) -;; ;; remove empty fragment -;; #(disj % #{}))}) - -;; ;; first gen needs to convert each attribute/objects into a set -;; (defn- ind2clustered-ctx -;; "This is a helper method to apply the by the individual specified clustering." -;; [args ctx {iobjs :objects iattr :attributes :as ind}] -;; (let [apply-cluster-obj (fn [tocluster-ctx cl] ((cluster-applier :objects (:obj-cl-quantifier args) tocluster-ctx) cl)) -;; apply-cluster-attr (fn [tocluster-ctx cl] ((cluster-applier :attributes (:attr-cl-quantifier args) tocluster-ctx) cl))] -;; (-> ctx -;; #(reduce apply-cluster-attr % iattr) -;; #(reduce apply-cluster-obj % iobjj)))) - -;; (defn- fill-individual-cluster -;; "Inserts as many objects/attributes to the individual as possible. -;; An individual is a set of nodes of the contexts incompatibility graph." -;; [args ctx {iobjs :objects iattr :attributes :as init-ind}] -;; (let [apply-cluster-obj (fn [tocluster-ctx cl] (if (coll? cl) ((cluster-applier :objects (:obj-cl-quantifier args) tocluster-ctx) cl) tocluster-ctx)) -;; apply-cluster-attr (fn [tocluster-ctx cl] (if (coll? cl) ((cluster-applier :attributes (:attr-cl-quantifier args) tocluster-ctx) cl) tocluster-ctx))] -;; (loop [ind (ind2clustered-ctx args ctx init-ind)] -;; ;; cluster until valid and 2D -;; )) -;; ) From 0303218f4ce730ef018cef00ce77767069061174 Mon Sep 17 00:00:00 2001 From: De Narm Date: Wed, 13 May 2020 21:03:13 +0200 Subject: [PATCH 026/117] Added Tikz support for measures --- src/main/clojure/conexp/io/smeasure.clj | 147 ++++++++++++++++++ src/test/clojure/conexp/fca/smeasure_test.clj | 26 ++++ 2 files changed, 173 insertions(+) create mode 100644 src/main/clojure/conexp/io/smeasure.clj diff --git a/src/main/clojure/conexp/io/smeasure.clj b/src/main/clojure/conexp/io/smeasure.clj new file mode 100644 index 000000000..5804e4554 --- /dev/null +++ b/src/main/clojure/conexp/io/smeasure.clj @@ -0,0 +1,147 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.io.smeasure + "Provides functionality to represent conexp-clj smeasures as latex code." + (:use conexp.base + conexp.fca.contexts + conexp.fca.smeasure + conexp.io.latex)) + +;;; Smeasure + +(declare smeasure->tikz) +(declare smeasure->lattice) + +(extend-type conexp.fca.smeasure.Smeasure + LaTeX + (latex + ([this] + (latex this :tikz)) + ([this choice] + (case choice + :tikz (smeasure->lattice this) + :lattice (smeasure->tikz this) + true (illegal-argument + "Unsupported latex format " choice " for contexts."))))) + +(defn- smeasure->tikz + [smeasure] + (let [ctx (context smeasure) + scale (scale smeasure) + mapping (measure smeasure) + ctx-obj (group-by #(mapping %) (objects ctx)) + sca-obj (objects scale) + sca-obj (loop [order (vec (difference (objects scale) + (keys ctx-obj))) + next (keys ctx-obj) + place (if (> (count (objects scale)) + (count (objects ctx))) + (int (/ (- (count (objects scale)) + (count (objects ctx))) + 2)) + 0)] + (if (empty? next) + order + (let [element (first next) + pos (+ place + (int + (/ (- (count (get ctx-obj element)) + 1) + 2))) + new-order (vec (concat (take pos order) + (list element) + (drop pos order))) + new-place (+ place (count (get ctx-obj element)))] + (recur new-order (drop 1 next) new-place))))] + (with-out-str + (println "%necessary tikz libraries") + (println "%\\usetikzlibrary{tikzmark,arrows,positioning}") + (println "\\begin{figure}") + (println " \\centering") + ;; + ;; original context + (println " \\begin{minipage}[c]{.5\\textwidth}") + (println " \\centering") + (println " \\begin{cxt}%") + (println " \\cxtName{}%") + (doseq [m (attributes ctx)] + (if (>= 2 (count (str m))) + (println (str " \\att{\\tikzmarknode{ca" (tex-escape m) + "}{" (tex-escape m) "}}%")) + (println (str " \\atr{\\tikzmarknode{ca" (tex-escape m) + "}{" (tex-escape m) "}}%")))) + (let [inz (incidence ctx)] + (doall + (for [[k objs] ctx-obj] + (doseq [g objs] + (print " \\obj{") + (doseq [m (attributes ctx)] + (print (if (inz [g m]) "x" "."))) + (println (str "}{" (tex-escape g) "}")))))) + (println " \\end{cxt}") + (println " \\end{minipage}%") + ;; + ;; scale context + (println " \\begin{minipage}[c]{.5\\textwidth}") + (println " \\centering") + (println " \\begin{cxt}%") + (println " \\cxtName{}%") + (doseq [m (attributes scale)] + (if (>= 2 (count (str m))) + (println (str " \\att{" (tex-escape m) "}%")) + (println (str " \\atr{" (tex-escape m) "}%")))) + (doall (let [inz (incidence scale)] + (doseq [g sca-obj] + (print " \\obj{") + (doseq [m (attributes scale)] + (print (if (inz [g m]) "x" "."))) + (println (str "}{\\tikzmarknode{so" (tex-escape g) + "}{" (tex-escape g) "}}"))))) + (println " \\end{cxt}") + (println " \\end{minipage}%") + (println "\\end{figure}") + ;; + ;; tikz overlay + (println "\\begin{tikzpicture}[overlay,remember picture]") + (let [ctx-obj-list (flatten (map second (vec ctx-obj))) + anchor (last (butlast (attributes ctx)))] + (doall (if (>= 2 (count (str anchor))) + (do + (println (str " \\node[right = 0.45cm of ca" + (tex-escape anchor) + "] (za) {};")) + (println (str " \\node[below = 0.25cm of za] (co" + (first ctx-obj-list) ") {};"))) + (println (str " \\node[below = 0.25cm of ca" + (tex-escape anchor) + "] (co" (first ctx-obj-list) ") {};")))) + (doall + (map + (fn[a b] + (println (str " \\node[below = 0.16cm of co" + (tex-escape a) + "] (co" (tex-escape b) ") {};"))) + ctx-obj-list + (drop 1 ctx-obj-list))) + (doall + (map + #(println (str " \\node[left = 0cm of so" % "](lso" % "){};")) + (objects scale))) + (doall + (for [obj ctx-obj-list] + (println (str " \\draw[->, >=stealth] (co" + (tex-escape obj) ") -- (lso" + (tex-escape (mapping obj)) ");"))))) + (println "\\end{tikzpicture}")))) + +;;; Smeasure + Lattice + +;;; + +nil diff --git a/src/test/clojure/conexp/fca/smeasure_test.clj b/src/test/clojure/conexp/fca/smeasure_test.clj index b197eb0fb..b89407a24 100644 --- a/src/test/clojure/conexp/fca/smeasure_test.clj +++ b/src/test/clojure/conexp/fca/smeasure_test.clj @@ -10,6 +10,32 @@ (:use conexp.fca.contexts conexp.fca.smeasure conexp.base) (:use clojure.test)) +(deftest test-smeasure-to-string + (let [ctx1 (make-context-nc #{1 2 3 4} #{1 2 3 4 5} + #{[1 1][2 2][1 3][2 4][3 5][4 1][4 3]}) + ctx2 (make-context-nc #{1 2 3} #{1 2 3 4 5} + #{[1 1][2 2][1 3][2 4][3 5]}) + sm1 (make-id-smeasure ctx1) + sm2 (make-smeasure ctx1 ctx2 #(case % 1 1 4 1 2 2 3 3))] + (is (= (smeasure-to-string sm1) + (str " |1 4 3 2 5 |1 4 3 2 5 \n" + "--+---------- --+----------\n" + "1 |x . x . . ⟶ 1 |x . x . . \n" + "--+---------- --+----------\n" + "4 |x . x . . ⟶ 4 |x . x . . \n" + "--+---------- --+----------\n" + "3 |. . . . x ⟶ 3 |. . . . x \n" + "--+---------- --+----------\n" + "2 |. x . x . ⟶ 2 |. x . x . \n"))) + (is (= (smeasure-to-string sm2) + (str " |1 4 3 2 5 |1 4 3 2 5 \n" + "--+---------- --+----------\n" + "1 |x . x . . ⟶ 1 |x . x . . \n" + "4 |x . x . . | \n" + "--+---------- --+----------\n" + "3 |. . . . x ⟶ 3 |. . . . x \n" + "--+---------- --+----------\n" + "2 |. x . x . ⟶ 2 |. x . x . \n"))))) (deftest test-remove-attributes (let [ctx (rand-context (range 6) 0.5) From 9103e64b3a07779e8c99a32f76ba964c9a4f5f9c Mon Sep 17 00:00:00 2001 From: De Narm Date: Thu, 14 May 2020 16:56:53 +0200 Subject: [PATCH 027/117] Added lattice tikz smeasure export --- src/main/clojure/conexp/io/latex.clj | 2 +- src/main/clojure/conexp/io/smeasure.clj | 177 ++++++++++++++++++- src/test/clojure/conexp/io/smeasure_test.clj | 50 ++++++ testing-data/latex/lattice-smeasure1-2.tex | 80 +++++++++ testing-data/latex/lattice-smeasure1-3.tex | 87 +++++++++ testing-data/latex/lattice-smeasure3-1.tex | 96 ++++++++++ testing-data/latex/tikz-smeasure1-2.tex | 48 +++++ testing-data/latex/tikz-smeasure1-3.tex | 60 +++++++ testing-data/latex/tikz-smeasure3-1.tex | 65 +++++++ 9 files changed, 661 insertions(+), 4 deletions(-) create mode 100644 src/test/clojure/conexp/io/smeasure_test.clj create mode 100644 testing-data/latex/lattice-smeasure1-2.tex create mode 100644 testing-data/latex/lattice-smeasure1-3.tex create mode 100644 testing-data/latex/lattice-smeasure3-1.tex create mode 100644 testing-data/latex/tikz-smeasure1-2.tex create mode 100644 testing-data/latex/tikz-smeasure1-3.tex create mode 100644 testing-data/latex/tikz-smeasure3-1.tex diff --git a/src/main/clojure/conexp/io/latex.clj b/src/main/clojure/conexp/io/latex.clj index 65724fe20..f94b20450 100644 --- a/src/main/clojure/conexp/io/latex.clj +++ b/src/main/clojure/conexp/io/latex.clj @@ -20,7 +20,7 @@ "Escapes all significant characters used by LaTeX." [string] (clojure.string/escape - string + (str string) {\& "\\&" \% "\\%" \$ "\\$" diff --git a/src/main/clojure/conexp/io/smeasure.clj b/src/main/clojure/conexp/io/smeasure.clj index 5804e4554..acc416988 100644 --- a/src/main/clojure/conexp/io/smeasure.clj +++ b/src/main/clojure/conexp/io/smeasure.clj @@ -10,7 +10,11 @@ "Provides functionality to represent conexp-clj smeasures as latex code." (:use conexp.base conexp.fca.contexts + conexp.fca.lattices conexp.fca.smeasure + [conexp.layouts.base :refer [positions nodes inf-irreducibles + sup-irreducibles connections annotation]] + conexp.layouts.dim-draw conexp.io.latex)) ;;; Smeasure @@ -25,8 +29,8 @@ (latex this :tikz)) ([this choice] (case choice - :tikz (smeasure->lattice this) - :lattice (smeasure->tikz this) + :tikz (smeasure->tikz this) + :lattice (smeasure->lattice this) true (illegal-argument "Unsupported latex format " choice " for contexts."))))) @@ -36,7 +40,6 @@ scale (scale smeasure) mapping (measure smeasure) ctx-obj (group-by #(mapping %) (objects ctx)) - sca-obj (objects scale) sca-obj (loop [order (vec (difference (objects scale) (keys ctx-obj))) next (keys ctx-obj) @@ -142,6 +145,174 @@ ;;; Smeasure + Lattice +(defn- smeasure->lattice + [smeasure] + (let [ctx (context smeasure) + scale (scale smeasure) + mapping (measure smeasure) + ctx-obj (group-by #(mapping %) (objects ctx))] + (with-out-str + (println "%necessary tikz libraries") + (println "%\\usetikzlibrary{tikzmark,arrows,positioning}") + (println "\\begin{figure}") + (println " \\centering") + ;; + ;; original context + (println " \\begin{minipage}[c]{.5\\textwidth}") + (println " \\centering") + (println " \\begin{cxt}%") + (println " \\cxtName{}%") + (doseq [m (attributes ctx)] + (if (>= 2 (count (str m))) + (println (str " \\att{\\tikzmarknode{ca" (tex-escape m) + "}{" (tex-escape m) "}}%")) + (println (str " \\atr{\\tikzmarknode{ca" (tex-escape m) + "}{" (tex-escape m) "}}%")))) + (let [inz (incidence ctx)] + (doall + (for [[k objs] ctx-obj] + (doseq [g objs] + (print " \\obj{") + (doseq [m (attributes ctx)] + (print (if (inz [g m]) "x" "."))) + (println (str "}{" (tex-escape g) "}")))))) + (println " \\end{cxt}") + (println " \\end{minipage}%") + ;; + ;; scale context + (println " \\begin{minipage}[c]{.5\\textwidth}") + (println " \\centering") + (let [layout (dim-draw-layout (concept-lattice scale)), + vertex-pos (positions layout), + sorted-vertices (sort #(let [[x_1 y_1] (vertex-pos %1), + [x_2 y_2] (vertex-pos %2)] + (or (< y_1 y_2) + (and (= y_1 y_2) + (< x_1 x_2)))) + (nodes layout)), + vertex-idx (into {} + (map-indexed (fn [i v] [v i]) + sorted-vertices))] + (println " \\colorlet{mivertexcolor}{blue}") + (println " \\colorlet{jivertexcolor}{red}") + (println " \\colorlet{vertexcolor}{mivertexcolor!50}") + (println " \\colorlet{bordercolor}{black!80}") + (println " \\colorlet{linecolor}{gray}") + (println (str " \\tikzset{vertexbase/.style={semithick, " + "shape=circle, inner sep=2pt, outer sep=0pt, " + "draw=bordercolor},%")) + (println " vertex/.style={vertexbase, fill=vertexcolor!45},%") + (println " mivertex/.style={vertexbase, fill=mivertexcolor!45},%") + (println " jivertex/.style={vertexbase, fill=jivertexcolor!45},%") + (println (str " divertex/.style={vertexbase, " + "top color=mivertexcolor!45, " + "bottom color=jivertexcolor!45},%")) + (println " conn/.style={-, thick, color=linecolor}%") + (println " }") + (println " \\begin{tikzpicture}") + (println " \\begin{scope} %for scaling and the like") + (println " \\begin{scope} %draw vertices") + (println (str " \\foreach \\nodename/\\nodetype/\\xpos/\\ypos" + " in {%")) + (let [infs (set (inf-irreducibles layout)), + sups (set (sup-irreducibles layout)), + insu (intersection infs sups), + vertex-lines (map (fn [v] + (let [i (vertex-idx v), + [x y] (vertex-pos v)] + (str " " i "/" + (cond + (contains? insu v) "divertex" + (contains? sups v) "jivertex" + (contains? infs v) "mivertex" + :else "vertex") + "/" x "/" y))) + sorted-vertices)] + (doseq [x (interpose ",\n" vertex-lines)] + (print x)) + (println)) + (println (str " } \\node[\\nodetype] (\\nodename) at " + "(\\xpos, \\ypos) {};")) + (println " \\end{scope}") + (println " \\begin{scope} %draw connections") + (doseq [[v w] (connections layout)] + (println (str " \\path (" (vertex-idx v) ") edge[conn] (" + (vertex-idx w) ");"))) + (println " \\end{scope}") + (println " \\begin{scope} %add labels") + (println (str " \\foreach " + "\\nodename/\\labelpos/\\labelopts/\\labelcontent " + "in {%")) + (let [ann (annotation layout), + ann-lines (mapcat (fn [v] + (let [[u l] (map tex-escape (ann v)), + lines (if-not (= "" u) + (list (str " " + (vertex-idx v) + "/above//{" u "}")) + ()), + lines (if-not (= "" l) + (conj + lines + (str " " + (vertex-idx v) + "/below//{" + (apply str + (map + #(str "\\tikzmarknode{n" % + "}{}") + (clojure.string/split + l + #", "))) + l "}")) + lines)] + lines)) + sorted-vertices)] + (doseq [x (interpose ",\n" ann-lines)] + (print x)) + (println)) + (println (str " } \\coordinate[label={[\\labelopts]\\labelpos" + ":{\\labelcontent}}](c) at (\\nodename);")) + (println " \\end{scope}") + (println " \\end{scope}") + (println " \\end{tikzpicture}")) + (println " \\end{minipage}%") + (println "\\end{figure}") + ;; + ;; tikz overlay + (println "\\begin{tikzpicture}[overlay,remember picture]") + (let [ctx-obj-list (flatten (map second (vec ctx-obj))) + anchor (last (butlast (attributes ctx)))] + (doall (if (>= 2 (count (str anchor))) + (do + (println (str " \\node[right = 0.45cm of ca" + (tex-escape anchor) + "] (za) {};")) + (println (str " \\node[below = 0.25cm of za] (co" + (first ctx-obj-list) ") {};"))) + (println (str " \\node[below = 0.25cm of ca" + (tex-escape anchor) + "] (co" (first ctx-obj-list) ") {};")))) + (doall + (map + (fn[a b] + (println (str " \\node[below = 0.16cm of co" + (tex-escape a) + "] (co" (tex-escape b) ") {};"))) + ctx-obj-list + (drop 1 ctx-obj-list))) + (doall + (map + #(println (str " \\node[above = 0.2cm of n" (tex-escape %) + "] (an" % ") {};")) + (objects scale))) + (doall + (for [obj ctx-obj-list] + (println (str " \\draw[->, >=stealth] (co" + (tex-escape obj) ") -- (an" + (tex-escape (mapping obj)) ");"))))) + (println "\\end{tikzpicture}")))) + ;;; nil diff --git a/src/test/clojure/conexp/io/smeasure_test.clj b/src/test/clojure/conexp/io/smeasure_test.clj new file mode 100644 index 000000000..94bff1078 --- /dev/null +++ b/src/test/clojure/conexp/io/smeasure_test.clj @@ -0,0 +1,50 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.io.smeasure-test + (:use conexp.base + [conexp.fca.contexts :refer [make-context-nc]] + conexp.fca.lattices + [conexp.fca.smeasure :refer [make-smeasure-nc]] + conexp.layouts.base + conexp.io.latex + conexp.io.smeasure) + (:use clojure.test)) + +;;; + +(def ctx1 (make-context-nc #{1 2 3 4} #{1 2 3 4 5} + #{[1 1][2 2][1 3][2 4][3 5][4 1][4 3]})) +(def ctx2 (make-context-nc #{1 2 3} #{1 2 3 4 5} #{[1 1][2 2][1 3][2 4][3 5]})) +(def ctx3 (make-context-nc #{1 2 3 4 5 6 7 8 9} #{1 2 3 4 5} + #{[1 1][2 2][1 3][2 4][3 5]})) + +(def sm1 (make-smeasure-nc ctx1 ctx2 #(case % 1 1 4 1 2 1 3 2))) +(def sm2 (make-smeasure-nc ctx1 ctx3 #(case % 1 1 4 1 2 1 3 2))) +(def sm3 (make-smeasure-nc ctx3 ctx1 + #(case % 1 1 4 1 2 1 3 2 5 1 6 2 7 1 8 4 9 3))) + +(deftest test-smeasure->tikz + (is (= (latex sm1 :tikz) + (slurp "testing-data/latex/tikz-smeasure1-2.tex"))) + (is (= (latex sm2 :tikz) + (slurp "testing-data/latex/tikz-smeasure1-3.tex"))) + (is (= (latex sm3 :tikz) + (slurp "testing-data/latex/tikz-smeasure3-1.tex")))) + +(deftest test-smeasure->tikz + (is (= (latex sm1 :lattice) + (slurp "testing-data/latex/lattice-smeasure1-2.tex"))) + (is (= (latex sm2 :lattice) + (slurp "testing-data/latex/lattice-smeasure1-3.tex"))) + (is (= (latex sm3 :lattice) + (slurp "testing-data/latex/lattice-smeasure3-1.tex")))) + +;;; + +nil diff --git a/testing-data/latex/lattice-smeasure1-2.tex b/testing-data/latex/lattice-smeasure1-2.tex new file mode 100644 index 000000000..ce05e0971 --- /dev/null +++ b/testing-data/latex/lattice-smeasure1-2.tex @@ -0,0 +1,80 @@ +%necessary tikz libraries +%\usetikzlibrary{tikzmark,arrows,positioning} +\begin{figure} + \centering + \begin{minipage}[c]{.5\textwidth} + \centering + \begin{cxt}% + \cxtName{}% + \att{\tikzmarknode{ca1}{1}}% + \att{\tikzmarknode{ca4}{4}}% + \att{\tikzmarknode{ca3}{3}}% + \att{\tikzmarknode{ca2}{2}}% + \att{\tikzmarknode{ca5}{5}}% + \obj{x.x..}{1} + \obj{x.x..}{4} + \obj{.x.x.}{2} + \obj{....x}{3} + \end{cxt} + \end{minipage}% + \begin{minipage}[c]{.5\textwidth} + \centering + \colorlet{mivertexcolor}{blue} + \colorlet{jivertexcolor}{red} + \colorlet{vertexcolor}{mivertexcolor!50} + \colorlet{bordercolor}{black!80} + \colorlet{linecolor}{gray} + \tikzset{vertexbase/.style={semithick, shape=circle, inner sep=2pt, outer sep=0pt, draw=bordercolor},% + vertex/.style={vertexbase, fill=vertexcolor!45},% + mivertex/.style={vertexbase, fill=mivertexcolor!45},% + jivertex/.style={vertexbase, fill=jivertexcolor!45},% + divertex/.style={vertexbase, top color=mivertexcolor!45, bottom color=jivertexcolor!45},% + conn/.style={-, thick, color=linecolor}% + } + \begin{tikzpicture} + \begin{scope} %for scaling and the like + \begin{scope} %draw vertices + \foreach \nodename/\nodetype/\xpos/\ypos in {% + 0/vertex/0/0, + 1/divertex/-2/4, + 2/divertex/0/4, + 3/divertex/2/4, + 4/vertex/0/8 + } \node[\nodetype] (\nodename) at (\xpos, \ypos) {}; + \end{scope} + \begin{scope} %draw connections + \path (1) edge[conn] (4); + \path (0) edge[conn] (1); + \path (0) edge[conn] (2); + \path (0) edge[conn] (3); + \path (2) edge[conn] (4); + \path (3) edge[conn] (4); + \end{scope} + \begin{scope} %add labels + \foreach \nodename/\labelpos/\labelopts/\labelcontent in {% + 1/below//{\tikzmarknode{n2}{}2}, + 1/above//{4, 2}, + 2/below//{\tikzmarknode{n1}{}1}, + 2/above//{1, 3}, + 3/below//{\tikzmarknode{n3}{}3}, + 3/above//{5} + } \coordinate[label={[\labelopts]\labelpos:{\labelcontent}}](c) at (\nodename); + \end{scope} + \end{scope} + \end{tikzpicture} + \end{minipage}% +\end{figure} +\begin{tikzpicture}[overlay,remember picture] + \node[right = 0.45cm of ca2] (za) {}; + \node[below = 0.25cm of za] (co1) {}; + \node[below = 0.16cm of co1] (co4) {}; + \node[below = 0.16cm of co4] (co2) {}; + \node[below = 0.16cm of co2] (co3) {}; + \node[above = 0.2cm of n1] (an1) {}; + \node[above = 0.2cm of n3] (an3) {}; + \node[above = 0.2cm of n2] (an2) {}; + \draw[->, >=stealth] (co1) -- (an1); + \draw[->, >=stealth] (co4) -- (an1); + \draw[->, >=stealth] (co2) -- (an1); + \draw[->, >=stealth] (co3) -- (an2); +\end{tikzpicture} diff --git a/testing-data/latex/lattice-smeasure1-3.tex b/testing-data/latex/lattice-smeasure1-3.tex new file mode 100644 index 000000000..af238f35e --- /dev/null +++ b/testing-data/latex/lattice-smeasure1-3.tex @@ -0,0 +1,87 @@ +%necessary tikz libraries +%\usetikzlibrary{tikzmark,arrows,positioning} +\begin{figure} + \centering + \begin{minipage}[c]{.5\textwidth} + \centering + \begin{cxt}% + \cxtName{}% + \att{\tikzmarknode{ca1}{1}}% + \att{\tikzmarknode{ca4}{4}}% + \att{\tikzmarknode{ca3}{3}}% + \att{\tikzmarknode{ca2}{2}}% + \att{\tikzmarknode{ca5}{5}}% + \obj{x.x..}{1} + \obj{x.x..}{4} + \obj{.x.x.}{2} + \obj{....x}{3} + \end{cxt} + \end{minipage}% + \begin{minipage}[c]{.5\textwidth} + \centering + \colorlet{mivertexcolor}{blue} + \colorlet{jivertexcolor}{red} + \colorlet{vertexcolor}{mivertexcolor!50} + \colorlet{bordercolor}{black!80} + \colorlet{linecolor}{gray} + \tikzset{vertexbase/.style={semithick, shape=circle, inner sep=2pt, outer sep=0pt, draw=bordercolor},% + vertex/.style={vertexbase, fill=vertexcolor!45},% + mivertex/.style={vertexbase, fill=mivertexcolor!45},% + jivertex/.style={vertexbase, fill=jivertexcolor!45},% + divertex/.style={vertexbase, top color=mivertexcolor!45, bottom color=jivertexcolor!45},% + conn/.style={-, thick, color=linecolor}% + } + \begin{tikzpicture} + \begin{scope} %for scaling and the like + \begin{scope} %draw vertices + \foreach \nodename/\nodetype/\xpos/\ypos in {% + 0/vertex/0/0, + 1/divertex/-2/4, + 2/divertex/0/4, + 3/divertex/2/4, + 4/vertex/0/8 + } \node[\nodetype] (\nodename) at (\xpos, \ypos) {}; + \end{scope} + \begin{scope} %draw connections + \path (1) edge[conn] (4); + \path (0) edge[conn] (1); + \path (0) edge[conn] (2); + \path (0) edge[conn] (3); + \path (2) edge[conn] (4); + \path (3) edge[conn] (4); + \end{scope} + \begin{scope} %add labels + \foreach \nodename/\labelpos/\labelopts/\labelcontent in {% + 1/below//{\tikzmarknode{n2}{}2}, + 1/above//{4, 2}, + 2/below//{\tikzmarknode{n1}{}1}, + 2/above//{1, 3}, + 3/below//{\tikzmarknode{n3}{}3}, + 3/above//{5}, + 4/below//{\tikzmarknode{n7}{}\tikzmarknode{n4}{}\tikzmarknode{n6}{}\tikzmarknode{n9}{}\tikzmarknode{n5}{}\tikzmarknode{n8}{}7, 4, 6, 9, 5, 8} + } \coordinate[label={[\labelopts]\labelpos:{\labelcontent}}](c) at (\nodename); + \end{scope} + \end{scope} + \end{tikzpicture} + \end{minipage}% +\end{figure} +\begin{tikzpicture}[overlay,remember picture] + \node[right = 0.45cm of ca2] (za) {}; + \node[below = 0.25cm of za] (co1) {}; + \node[below = 0.16cm of co1] (co4) {}; + \node[below = 0.16cm of co4] (co2) {}; + \node[below = 0.16cm of co2] (co3) {}; + \node[above = 0.2cm of n7] (an7) {}; + \node[above = 0.2cm of n1] (an1) {}; + \node[above = 0.2cm of n4] (an4) {}; + \node[above = 0.2cm of n6] (an6) {}; + \node[above = 0.2cm of n3] (an3) {}; + \node[above = 0.2cm of n2] (an2) {}; + \node[above = 0.2cm of n9] (an9) {}; + \node[above = 0.2cm of n5] (an5) {}; + \node[above = 0.2cm of n8] (an8) {}; + \draw[->, >=stealth] (co1) -- (an1); + \draw[->, >=stealth] (co4) -- (an1); + \draw[->, >=stealth] (co2) -- (an1); + \draw[->, >=stealth] (co3) -- (an2); +\end{tikzpicture} diff --git a/testing-data/latex/lattice-smeasure3-1.tex b/testing-data/latex/lattice-smeasure3-1.tex new file mode 100644 index 000000000..9f2ce0dd6 --- /dev/null +++ b/testing-data/latex/lattice-smeasure3-1.tex @@ -0,0 +1,96 @@ +%necessary tikz libraries +%\usetikzlibrary{tikzmark,arrows,positioning} +\begin{figure} + \centering + \begin{minipage}[c]{.5\textwidth} + \centering + \begin{cxt}% + \cxtName{}% + \att{\tikzmarknode{ca1}{1}}% + \att{\tikzmarknode{ca4}{4}}% + \att{\tikzmarknode{ca3}{3}}% + \att{\tikzmarknode{ca2}{2}}% + \att{\tikzmarknode{ca5}{5}}% + \obj{.....}{7} + \obj{x.x..}{1} + \obj{.....}{4} + \obj{.x.x.}{2} + \obj{.....}{5} + \obj{.....}{6} + \obj{....x}{3} + \obj{.....}{9} + \obj{.....}{8} + \end{cxt} + \end{minipage}% + \begin{minipage}[c]{.5\textwidth} + \centering + \colorlet{mivertexcolor}{blue} + \colorlet{jivertexcolor}{red} + \colorlet{vertexcolor}{mivertexcolor!50} + \colorlet{bordercolor}{black!80} + \colorlet{linecolor}{gray} + \tikzset{vertexbase/.style={semithick, shape=circle, inner sep=2pt, outer sep=0pt, draw=bordercolor},% + vertex/.style={vertexbase, fill=vertexcolor!45},% + mivertex/.style={vertexbase, fill=mivertexcolor!45},% + jivertex/.style={vertexbase, fill=jivertexcolor!45},% + divertex/.style={vertexbase, top color=mivertexcolor!45, bottom color=jivertexcolor!45},% + conn/.style={-, thick, color=linecolor}% + } + \begin{tikzpicture} + \begin{scope} %for scaling and the like + \begin{scope} %draw vertices + \foreach \nodename/\nodetype/\xpos/\ypos in {% + 0/vertex/0/0, + 1/divertex/-2/4, + 2/divertex/0/4, + 3/divertex/2/4, + 4/vertex/0/8 + } \node[\nodetype] (\nodename) at (\xpos, \ypos) {}; + \end{scope} + \begin{scope} %draw connections + \path (1) edge[conn] (4); + \path (2) edge[conn] (4); + \path (0) edge[conn] (1); + \path (0) edge[conn] (2); + \path (0) edge[conn] (3); + \path (3) edge[conn] (4); + \end{scope} + \begin{scope} %add labels + \foreach \nodename/\labelpos/\labelopts/\labelcontent in {% + 1/below//{\tikzmarknode{n2}{}2}, + 1/above//{4, 2}, + 2/below//{\tikzmarknode{n1}{}\tikzmarknode{n4}{}1, 4}, + 2/above//{1, 3}, + 3/below//{\tikzmarknode{n3}{}3}, + 3/above//{5} + } \coordinate[label={[\labelopts]\labelpos:{\labelcontent}}](c) at (\nodename); + \end{scope} + \end{scope} + \end{tikzpicture} + \end{minipage}% +\end{figure} +\begin{tikzpicture}[overlay,remember picture] + \node[right = 0.45cm of ca2] (za) {}; + \node[below = 0.25cm of za] (co7) {}; + \node[below = 0.16cm of co7] (co1) {}; + \node[below = 0.16cm of co1] (co4) {}; + \node[below = 0.16cm of co4] (co2) {}; + \node[below = 0.16cm of co2] (co5) {}; + \node[below = 0.16cm of co5] (co6) {}; + \node[below = 0.16cm of co6] (co3) {}; + \node[below = 0.16cm of co3] (co9) {}; + \node[below = 0.16cm of co9] (co8) {}; + \node[above = 0.2cm of n1] (an1) {}; + \node[above = 0.2cm of n4] (an4) {}; + \node[above = 0.2cm of n3] (an3) {}; + \node[above = 0.2cm of n2] (an2) {}; + \draw[->, >=stealth] (co7) -- (an1); + \draw[->, >=stealth] (co1) -- (an1); + \draw[->, >=stealth] (co4) -- (an1); + \draw[->, >=stealth] (co2) -- (an1); + \draw[->, >=stealth] (co5) -- (an1); + \draw[->, >=stealth] (co6) -- (an2); + \draw[->, >=stealth] (co3) -- (an2); + \draw[->, >=stealth] (co9) -- (an3); + \draw[->, >=stealth] (co8) -- (an4); +\end{tikzpicture} diff --git a/testing-data/latex/tikz-smeasure1-2.tex b/testing-data/latex/tikz-smeasure1-2.tex new file mode 100644 index 000000000..6f91c8eea --- /dev/null +++ b/testing-data/latex/tikz-smeasure1-2.tex @@ -0,0 +1,48 @@ +%necessary tikz libraries +%\usetikzlibrary{tikzmark,arrows,positioning} +\begin{figure} + \centering + \begin{minipage}[c]{.5\textwidth} + \centering + \begin{cxt}% + \cxtName{}% + \att{\tikzmarknode{ca1}{1}}% + \att{\tikzmarknode{ca4}{4}}% + \att{\tikzmarknode{ca3}{3}}% + \att{\tikzmarknode{ca2}{2}}% + \att{\tikzmarknode{ca5}{5}}% + \obj{x.x..}{1} + \obj{x.x..}{4} + \obj{.x.x.}{2} + \obj{....x}{3} + \end{cxt} + \end{minipage}% + \begin{minipage}[c]{.5\textwidth} + \centering + \begin{cxt}% + \cxtName{}% + \att{1}% + \att{4}% + \att{3}% + \att{2}% + \att{5}% + \obj{....x}{\tikzmarknode{so3}{3}} + \obj{x.x..}{\tikzmarknode{so1}{1}} + \obj{.x.x.}{\tikzmarknode{so2}{2}} + \end{cxt} + \end{minipage}% +\end{figure} +\begin{tikzpicture}[overlay,remember picture] + \node[right = 0.45cm of ca2] (za) {}; + \node[below = 0.25cm of za] (co1) {}; + \node[below = 0.16cm of co1] (co4) {}; + \node[below = 0.16cm of co4] (co2) {}; + \node[below = 0.16cm of co2] (co3) {}; + \node[left = 0cm of so1](lso1){}; + \node[left = 0cm of so3](lso3){}; + \node[left = 0cm of so2](lso2){}; + \draw[->, >=stealth] (co1) -- (lso1); + \draw[->, >=stealth] (co4) -- (lso1); + \draw[->, >=stealth] (co2) -- (lso1); + \draw[->, >=stealth] (co3) -- (lso2); +\end{tikzpicture} diff --git a/testing-data/latex/tikz-smeasure1-3.tex b/testing-data/latex/tikz-smeasure1-3.tex new file mode 100644 index 000000000..045a672d0 --- /dev/null +++ b/testing-data/latex/tikz-smeasure1-3.tex @@ -0,0 +1,60 @@ +%necessary tikz libraries +%\usetikzlibrary{tikzmark,arrows,positioning} +\begin{figure} + \centering + \begin{minipage}[c]{.5\textwidth} + \centering + \begin{cxt}% + \cxtName{}% + \att{\tikzmarknode{ca1}{1}}% + \att{\tikzmarknode{ca4}{4}}% + \att{\tikzmarknode{ca3}{3}}% + \att{\tikzmarknode{ca2}{2}}% + \att{\tikzmarknode{ca5}{5}}% + \obj{x.x..}{1} + \obj{x.x..}{4} + \obj{.x.x.}{2} + \obj{....x}{3} + \end{cxt} + \end{minipage}% + \begin{minipage}[c]{.5\textwidth} + \centering + \begin{cxt}% + \cxtName{}% + \att{1}% + \att{4}% + \att{3}% + \att{2}% + \att{5}% + \obj{.....}{\tikzmarknode{so7}{7}} + \obj{.....}{\tikzmarknode{so4}{4}} + \obj{.....}{\tikzmarknode{so6}{6}} + \obj{x.x..}{\tikzmarknode{so1}{1}} + \obj{....x}{\tikzmarknode{so3}{3}} + \obj{.x.x.}{\tikzmarknode{so2}{2}} + \obj{.....}{\tikzmarknode{so9}{9}} + \obj{.....}{\tikzmarknode{so5}{5}} + \obj{.....}{\tikzmarknode{so8}{8}} + \end{cxt} + \end{minipage}% +\end{figure} +\begin{tikzpicture}[overlay,remember picture] + \node[right = 0.45cm of ca2] (za) {}; + \node[below = 0.25cm of za] (co1) {}; + \node[below = 0.16cm of co1] (co4) {}; + \node[below = 0.16cm of co4] (co2) {}; + \node[below = 0.16cm of co2] (co3) {}; + \node[left = 0cm of so7](lso7){}; + \node[left = 0cm of so1](lso1){}; + \node[left = 0cm of so4](lso4){}; + \node[left = 0cm of so6](lso6){}; + \node[left = 0cm of so3](lso3){}; + \node[left = 0cm of so2](lso2){}; + \node[left = 0cm of so9](lso9){}; + \node[left = 0cm of so5](lso5){}; + \node[left = 0cm of so8](lso8){}; + \draw[->, >=stealth] (co1) -- (lso1); + \draw[->, >=stealth] (co4) -- (lso1); + \draw[->, >=stealth] (co2) -- (lso1); + \draw[->, >=stealth] (co3) -- (lso2); +\end{tikzpicture} diff --git a/testing-data/latex/tikz-smeasure3-1.tex b/testing-data/latex/tikz-smeasure3-1.tex new file mode 100644 index 000000000..eabe4b978 --- /dev/null +++ b/testing-data/latex/tikz-smeasure3-1.tex @@ -0,0 +1,65 @@ +%necessary tikz libraries +%\usetikzlibrary{tikzmark,arrows,positioning} +\begin{figure} + \centering + \begin{minipage}[c]{.5\textwidth} + \centering + \begin{cxt}% + \cxtName{}% + \att{\tikzmarknode{ca1}{1}}% + \att{\tikzmarknode{ca4}{4}}% + \att{\tikzmarknode{ca3}{3}}% + \att{\tikzmarknode{ca2}{2}}% + \att{\tikzmarknode{ca5}{5}}% + \obj{.....}{7} + \obj{x.x..}{1} + \obj{.....}{4} + \obj{.x.x.}{2} + \obj{.....}{5} + \obj{.....}{6} + \obj{....x}{3} + \obj{.....}{9} + \obj{.....}{8} + \end{cxt} + \end{minipage}% + \begin{minipage}[c]{.5\textwidth} + \centering + \begin{cxt}% + \cxtName{}% + \att{1}% + \att{4}% + \att{3}% + \att{2}% + \att{5}% + \obj{x.x..}{\tikzmarknode{so1}{1}} + \obj{.x.x.}{\tikzmarknode{so2}{2}} + \obj{....x}{\tikzmarknode{so3}{3}} + \obj{x.x..}{\tikzmarknode{so4}{4}} + \end{cxt} + \end{minipage}% +\end{figure} +\begin{tikzpicture}[overlay,remember picture] + \node[right = 0.45cm of ca2] (za) {}; + \node[below = 0.25cm of za] (co7) {}; + \node[below = 0.16cm of co7] (co1) {}; + \node[below = 0.16cm of co1] (co4) {}; + \node[below = 0.16cm of co4] (co2) {}; + \node[below = 0.16cm of co2] (co5) {}; + \node[below = 0.16cm of co5] (co6) {}; + \node[below = 0.16cm of co6] (co3) {}; + \node[below = 0.16cm of co3] (co9) {}; + \node[below = 0.16cm of co9] (co8) {}; + \node[left = 0cm of so1](lso1){}; + \node[left = 0cm of so4](lso4){}; + \node[left = 0cm of so3](lso3){}; + \node[left = 0cm of so2](lso2){}; + \draw[->, >=stealth] (co7) -- (lso1); + \draw[->, >=stealth] (co1) -- (lso1); + \draw[->, >=stealth] (co4) -- (lso1); + \draw[->, >=stealth] (co2) -- (lso1); + \draw[->, >=stealth] (co5) -- (lso1); + \draw[->, >=stealth] (co6) -- (lso2); + \draw[->, >=stealth] (co3) -- (lso2); + \draw[->, >=stealth] (co9) -- (lso3); + \draw[->, >=stealth] (co8) -- (lso4); +\end{tikzpicture} From 83c6f816272d4a3687b75e359fdcda7e16967124 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Mon, 18 May 2020 18:57:52 +0200 Subject: [PATCH 028/117] Now with genetic clustering --- src/main/clojure/conexp/fca/smeasure.clj | 358 ++++++++++++++--------- 1 file changed, 225 insertions(+), 133 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index db2c59abc..3333777d9 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -99,6 +99,32 @@ (incidence s))] (make-smeasure-nc (context sm) new-scale (measure sm)))) +(defmulti rename-scale + "Renames objects or attributes in the scale. Input the renaming as function on the + set of objects or as key value pairs." + (fn [type & args] type)) +(alter-meta! #'rename-scale assoc :private true) + +(defmethod rename-scale :objects + ([_ sm rename-fn] + (make-smeasure-nc (context sm) + (rename-objects (scale sm) rename-fn) + (comp rename-fn (measure sm)))) + ([_ sm key val & keyvals] + (let [rename-map (apply hash-map key val keyvals) + rename-fn (fn [o] (or (get rename-map o) o))] + (rename-scale :objects sm rename-fn)))) + +(defmethod rename-scale :attributes + ([_ sm rename-fn] + (make-smeasure-nc (context sm) + (rename-attributes (scale sm) rename-fn) + (measure sm))) + ([_ sm key val & keyvals] + (let [rename-map (apply hash-map key val keyvals) + rename-fn (fn [a] (or (get rename-map a) a))] + (rename-scale :attributes sm rename-fn)))) + (defn- valid-cluster "This function is a predicate factory for valid scale measure clustering." [scale original] @@ -120,49 +146,52 @@ (defmethod cluster-applier [:attributes :ex] [_ _ ctx] - (fn [attr] (make-context (objects ctx) - (conj (difference (attributes ctx) attr) attr) - (fn [a b] - (if (set? b) - (some #((incidence ctx) [a %]) - b) - ((incidence ctx) [a b])))))) - -(defmethod cluster-applier [:attributes :ex] + (let [i (incidence-relation ctx)] + (fn [attr] (make-context (objects ctx) + (conj (difference (attributes ctx) attr) attr) + (fn [a b] + (if (= attr b) + (some #((incidence ctx) [a %]) + b) + ((incidence ctx) [a b]))))))) + +(defmethod cluster-applier [:attributes :all] [_ _ ctx] - (fn [attr] - (make-context (objects ctx) - (conj (difference (set (attributes ctx)) attr) - attr) - (fn [a b] - (if (set? b) - (every? #((incidence ctx) [a %]) - b) - ((incidence ctx) [a b])))))) + (let [i (incidence-relation ctx)] + (fn [attr] + (make-context (objects ctx) + (conj (difference (set (attributes ctx)) attr) + attr) + (fn [a b] + (if (= attr b) + (every? #((incidence ctx) [a %]) + b) + ((incidence ctx) [a b]))))))) (defmethod cluster-applier [:objects :all] [_ _ ctx] (fn [obj] (make-context (conj (difference (objects ctx) obj) obj) - (attributes ctx) - (fn [a b] - (if (set? a) - (every? #((incidence ctx) [% b]) - a) - ((incidence ctx) [a b])))))) + (attributes ctx) + (fn [a b] + (if (= a obj) + (every? #((incidence ctx) [% b]) + a) + ((incidence ctx) [a b])))))) + (defmethod cluster-applier [:objects :ex] [_ _ ctx] (fn [obj] (make-context (conj (difference (objects ctx) obj) obj) - (attributes ctx) - (fn [a b] - (if (set? a) - (some #((incidence ctx) [% b]) - a) - ((incidence ctx) [a b])))))) + (attributes ctx) + (fn [a b] + (if (= obj a) + (some #((incidence ctx) [% b]) + a) + ((incidence ctx) [a b])))))) + (defn- flattened-cluster-applier "Returns a cluster method depending on the 'kind and 'quant specifier." [ctx kind quant] - (fn [cl] (-> cl - (cluster-applier kind quant ctx) + (fn [cl] (-> ((cluster-applier kind quant ctx) cl) (rename-objects (fn [o] (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) #{} o))) @@ -258,9 +287,9 @@ (if (coll? result) (map (partial reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) #{}) result) - (rename kind (fn [k] - (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) - #{} k)))))) + (rename-scale kind result (fn [k] + (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) + #{} k)))))) (defmulti repair-cluster "Given a scale context constructs a valid smeasure scale by using as @@ -269,60 +298,28 @@ (fn [quantifier & args] quantifier)) (alter-meta! #'repair-cluster assoc :private true) -(defmethod repair-cluster :all - [_ ctx broken-scale] - (let [br-exts (map #(hash-map :new ((comp first object-concept) %) :obj %) (objects broken-scale)) ; TODO sufficient? all attributes are valid for :all - pre-images (sort-by count - (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat - br-exts)) - not-closed? (fn [e] (let [orig-e (context-object-closure ctx (:new e))] - (if (= orig-e e) false (assoc e :original orig-e)))) - image (fn [o] (some - #(if (contains? % o) % false) (objects broken-scale))) - broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality - (if broken - (let [apply-flattened-cluster (flattened-cluster-applier :objects :all broken-scale) - missing (map image (difference (:original broken) (:new broken))) - tocluster (conj (reduce conj #{} missing) (:obj broken))] - (repair-cluster :all ctx (apply-flattened-cluster broken-scale tocluster))) - broken-scale))) +(defmethod repair-cluster :all ;; todo stackoverflow + [_ ctx s] + (loop [broken-scale s] + (let [br-exts (extents broken-scale) + pre-images (sort-by count + (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat + br-exts)) + not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] + (if (= orig-e e) nil orig-e))) + image (fn [o] (some + #(if (contains? % o) % false) (objects broken-scale))) + broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality + (if broken + (let [apply-flattened-cluster (flattened-cluster-applier broken-scale :objects :all) + fixed-extent (reduce conj #{} (map image broken))] + (recur (apply-flattened-cluster fixed-extent))) + broken-scale)))) ;; (defmethod repair-cluster :ex ;; [_ ctx broken-scale] ;; TODO) - -(defmulti rename-scale - "Renames objects or attributes in the scale. Input the renaming as function on the - set of objects or as key value pairs." - (fn [type & args] type)) -(alter-meta! #'rename-scale assoc :private true) - -(defmethod rename-scale :objects - ([_ sm rename-fn] - (make-smeasure-nc (context sm) - (rename-objects (scale sm) rename-fn) - (comp rename-fn (measure sm)))) - ([_ sm key val & keyvals] - (let [rename-map (apply hash-map key val keyvals) - rename-fn (fn [o] (or (get rename-map o) o))] - (rename-scale :objects sm rename-fn)))) - -(defmethod rename-scale :attributes - ([sm rename-fn] - (make-smeasure-nc (context sm) - (rename-attributes (scale sm) rename-fn) - (measure sm))) - ([sm key val & keyvals] - (let [rename-map (apply hash-map key val keyvals) - rename-fn (fn [a] (or (get rename-map a) a))] - (rename-scale :attributes sm rename-fn)))) - - -; todo 2D begriffsverband wenn nicht kreuz graph bipartite -; rotes buch Satz 36 page 134 -; Genau dann ist die Ferrersdimension von (G, M, I) höchstens zwei, wenn der Un- -; verträglichkeitsgraph bipartit ist. (defn- incompatibility-graph "For a formal context computes the imcompatibility graph of its incidence relation." @@ -381,18 +378,18 @@ {iobjs2 :objects iattr2 :attributes :as ind2}] {:objects (->> iobjs2 ;; computes splitance - (reduce (fn [tmp-ind cl] (union (map #(difference % cl) tmp-ind) - (map #(intersection % cl) tmp-ind))) + (reduce (fn [tmp-ind cl] (union (set (map #(difference % cl) tmp-ind)) + (set (map #(intersection % cl) tmp-ind)))) iobjs1) ;; remove empty fragment - #(disj % #{})) + (#(disj % #{}))) :attributes (->> iattr2 ;; computes splitance - (reduce (fn [tmp-ind cl] (union (map #(difference % cl) tmp-ind) - (map #(intersection % cl) tmp-ind))) + (reduce (fn [tmp-ind cl] (union (set (map #(difference % cl) tmp-ind)) + (set (map #(intersection % cl) tmp-ind)))) iattr1) ;; remove empty fragment - #(disj % #{}))}) + (#(disj % #{})))}) ;; first gen needs to convert each attribute/objects into a set (defn- ind2clustered-ctx @@ -400,38 +397,37 @@ [args ctx {iobjs :objects iattr :attributes :as ind}] (let [apply-cluster-obj (fn [tocluster-ctx cl] ((cluster-applier :objects (:obj-cl-quantifier args) tocluster-ctx) cl)) apply-cluster-attr (fn [tocluster-ctx cl] ((cluster-applier :attributes (:attr-cl-quantifier args) tocluster-ctx) cl))] - (-> ctx - #(reduce apply-cluster-attr % iattr) - #(reduce apply-cluster-obj % iobjj)))) + (reduce apply-cluster-obj (reduce apply-cluster-attr ctx iattr) + iobjs))) (defn- apply-small-rand-cluster "This is a helper method to apply the smallest clustering out of a few random valid clusterings." - [args scale] - (let [candidates (if (rand-nth [true false]) - (zip (repeat :object) - (take 3 (partition 2 (shuffle (objects ctx))))) - (zip (repeat :attribute) - (take 3 (partition 2 (shuffle (attributes ctx)))))) - ;; how large the clusters become - key-fkt (fn [[kind thing]] - (let [result (flattened-cluster kind (:quantifier args) - (make-smeasure-nc (:ctx args) scale - (fn [o] - (some #(if (contains? % o) % false) - (objects broken-scale)))) - thing)] - (if (coll? result) (count (first)) - (apply + (map count thing))))) - smallest (min-key key-fkt candidates) - ] - (-> (flattened-cluster (first smallest) (:quantifier args) - (make-smeasure-nc (:ctx args) scale - (fn [o] - (some - #(if (contains? % o) % false) - (objects broken-scale)))) - (second smallest))))) + [args ctx scale-ctx] + (let [kind (rand-nth [:attributes :objects]) + quant (if (= :attributes kind) + (:attr-cl-quantifier args) + (:obj-cl-quantifier args)) + candidates (if (= :objects kind) + (map set (take 3 (partition 2 (shuffle (objects scale-ctx))))) + (map set (take 3 (partition 2 (shuffle (attributes scale-ctx)))))) + ;; how large the clusters get + sm (make-smeasure-nc ctx scale-ctx + (fn [o] + (some + #(if (contains? % o) % false) + (objects scale-ctx)))) + key-fkt (fn [thing] + (let [result (flattened-cluster kind + quant + sm thing)] + (if (coll? result) (count (first result)) + (apply + (map count thing))))) + smallest (apply min-key key-fkt candidates) + flat-clustered (cluster kind quant sm smallest)] + (if (coll? flat-clustered) ;;clustering was not valid, but returned a list of valid superclusters + (scale (flattened-cluster kind quant sm (first flat-clustered))) + (scale (flattened-cluster kind quant sm smallest))))) (defn- fill-individual-cluster "Inserts as many objects/attributes to the individual as possible. @@ -439,14 +435,13 @@ [args ctx {iobjs :objects iattr :attributes :as ind}] (let [repaired-ind (->> ind (ind2clustered-ctx args ctx) - (repair-cluster :all)) + (repair-cluster :all ctx)) make-ind-map #(hash-map :objects (objects %) :attributes (attributes %)) - 2dcontext? (comp la/bipartite? incompatibility-graph) - apply-rand-cluster (fn [c] (flattened-cluster-applier :objects :all c))] + context2d? (comp la/bipartite? incompatibility-graph)] (loop [tmp-ind repaired-ind] ;; apply small clusters until 2D - (if (2dcontext? tmp-ind) + (if (context2d? tmp-ind) (make-ind-map tmp-ind) - (recur (apply-small-rand-cluster args)))))) + (recur (apply-small-rand-cluster args ctx tmp-ind)))))) (defn- fill-individual "Inserts as many objects/attributes to the individual as possible. @@ -472,12 +467,17 @@ (defn- make-args-map "Returns default args updated by user input." [args] - (let [default-args {:generation-size 30 :generations 30 + (let [default-args {:generation-size 30 :generations 10 :survival-ratio 0.1 :mutation-rate 0.3 - :fresh-chance 0.05 - :init {:objects #{} :attributes #{}}}] - (assert (and (:init args) - (not (la/bipartite? (incompatibility-graph (:init args))))) + :fresh-chance 0.05 :mode :incidence-clustered + :obj-cl-quantifier :all + :attr-cl-quantifier :all + :init {:objects #{} :attributes #{}} + :init-cluster (fn [ctx] + {:objects (reduce #(conj %1 #{%2}) #{} (objects ctx)) + :attributes (reduce #(conj %1 #{%2}) #{} (attributes ctx))})}] + (assert (or (not (:init args)) + (la/bipartite? (incompatibility-graph (:init args)))) "Inputted initial Context must have a concept lattice of order dimension two.") (let [combined-args @@ -485,19 +485,19 @@ (update :init #(if (context? %) {:objects (objects %) :attributes (attributes %)} %)))] - (assoc :survival-count (int (* (:generation-size combined-args) + (assoc combined-args :survival-count (int (* (:generation-size combined-args) (:survival-ratio combined-args))))))) (defmulti fitness "For a bipartite incompatibility graph of a subset of attributes and objects of a context, computes if adding an object/attribute preserves the bipartite property." - (fn [& args] (:mode (first args)))) + (fn [args & params] (:mode args))) (alter-meta! #'fitness assoc :private true) (defmethod fitness :clustered - [& args] - (apply fitness args)) + [_ & args] + (apply fitness :default args)) (defmethod fitness :concepts [_ ctx {iobjs :objects iattr :attributes :as ind}] @@ -505,6 +505,12 @@ concepts count)) +(defmethod fitness :concepts-cluster + [args ctx {iobjs :objects iattr :attributes :as ind}] + (-> (ind2clustered-ctx args ctx ind) + concepts + count)) + (defmethod fitness :ctx-nontrivia [_ ctx {iobjs :objects iattr :attributes :as ind}] (let [sub-ctx (make-context iobjs iattr (incidence ctx)) @@ -515,16 +521,48 @@ (* (count nontrivia-obj) (count nontrivia-attr)))) +(defmethod fitness :nontrivia-clustered + [args ctx {iobjs :objects iattr :attributes :as ind}] + (let [sub-ctx (ind2clustered-ctx args ctx ind) + nontrivia-obj (filter #(not (empty? (object-derivation sub-ctx #{%}))) + (objects sub-ctx)) + nontrivia-attr (filter #(not (empty? (attribute-derivation sub-ctx #{%}))) + (attributes sub-ctx))] + (* (count nontrivia-obj) + (count nontrivia-attr)))) + + (defmethod fitness :incidence [_ ctx {iobjs :objects iattr :attributes :as ind}] (let [sub-ctx (make-context iobjs iattr (incidence ctx))] (count (incidence-relation sub-ctx)))) +(defmethod fitness :incidence-clustered + [args ctx {iobjs :objects iattr :attributes :as ind}] + (let [sub-ctx (ind2clustered-ctx args ctx ind)] + (count (incidence-relation sub-ctx)))) + (defmethod fitness :default [_ ctx {iobjs :objects iattr :attributes :as ind}] (* (count iobjs) (count iattr))) +(defn- mutation-cluster + "Mutates the current individual by removing an object or attribute + given a probability." + [args ctx {iobjs :objects iattr :attributes :as ind}] + (if (> (:fresh-chance args) (rand)) + (fill-individual-cluster args ctx ((:init-cluster args) ctx)) + (let [mutated-obj (into #{} (random-sample (:mutation-rate args) iobjs)) + mutated-attr (into #{} (random-sample (:mutation-rate args) iattr))] + (-> ind + (assoc :objects (reduce (fn [ind-objs tomutate-obj-cl] ;; flattens the to mutate cluster #{1 2 3} -> #{1} #{2} #{3} + (reduce #(conj %1 #{%2}) ind-objs tomutate-obj-cl)) + (difference (:objects ind) mutated-obj) mutated-obj)) + (assoc :attributes (reduce (fn [ind-attr tomutate-attr-cl] + (reduce #(conj %1 #{%2}) ind-attr tomutate-attr-cl)) + (difference (:attributes ind) mutated-attr) mutated-attr)))))) + (defn- mutation "Mutates the current individual by removing an object or attribute given a probability." @@ -537,6 +575,16 @@ (assoc :objects mutated-obj) (assoc :attributes mutated-attr))))) +(defn- breeding-cluster + "Given two individuals, i.e. contexts, breeds a next new individual by + first computing the context of common attributes and + objects. Secondly as many attributes/objects of ctx are inserted + without increasing the order dimension of the new individual." + [args ctx ind1 ind2] + (->> (cluster-ind-intersecter ind1 ind2) + (mutation-cluster args ctx) + (fill-individual-cluster args ctx))) + (defn- breeding "Given two individuals, i.e. contexts, breeds a next new individual by first computing the context of common attributes and @@ -548,6 +596,26 @@ (mutation args ctx graph) (fill-individual ctx graph))) +(defn- next-generation-cluster + "Given the current generation of contexts, breeds the next generation." + [args ctx generation] + (let [fitness-vals (->> generation + (sort-by (partial fitness args ctx)) + (take (:survival-count args))) + survivals (take (:survival-count args) fitness-vals) + pairing (->> survivals + shuffle + (partition 2)) + rand-pair (fn [] (->> survivals + shuffle + (take 2)))] + (into [] + (concat survivals + (->> (concat pairing (repeat (rand-pair))) + (take (- (:generation-size args) (:survival-count args))) + (into []) + (map (fn [[ind1 ind2]] (breeding-cluster args ctx ind1 ind2)))))))) + (defn- next-generation "Given the current generation of contexts, breeds the next generation." [args ctx graph generation] @@ -568,16 +636,40 @@ (into []) (map #(apply breeding args ctx graph %))))))) +(defn- first-generation-cluster + "Computes a first random generation of contexts with order dimension + at most two." + [args ctx] + (into [] + (for [i (range (:generation-size args))] + (fill-individual-cluster args ctx + ((:init-cluster args) ctx))))) + (defn- first-generation "Computes a first random generation of contexts with order dimension at most two." [args ctx graph] (into [] - (for [_ (range (:generation-size args))] + (for [i (range (:generation-size args))] (fill-individual ctx graph (:init args))))) +(defn genetic-2d-cluster + "Genetic algorithm to determine a maximal sub-context with order + dimension at most two. Maximal in terms of number of objects times + number of attributes." + [ctx & [args]] + (let [args (make-args-map (if (nil? args) {} args))] + (loop [n (:generations args) + generation (first-generation-cluster args ctx)] + (println "Generation: " (- (:generations args) n)) + (if (= n 0) + (->> generation + (apply max-key (partial fitness args ctx)) + (ind2clustered-ctx args ctx)) + (recur (dec n) (next-generation-cluster args ctx generation)))))) + (defn genetic-2d-subctx "Genetic algorithm to determine a maximal sub-context with order dimension at most two. Maximal in terms of number of objects times From c35e9e5943e1d9940b0f9489d6c64d1ae5d7d6cf Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 19 May 2020 11:09:21 +0200 Subject: [PATCH 029/117] bugfix --- src/main/clojure/conexp/fca/smeasure.clj | 67 +++++++++++++++++------- 1 file changed, 47 insertions(+), 20 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 3333777d9..3e873f7f4 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -208,6 +208,7 @@ (let [candidates (build-candidates i) valids (filter valid-cluster? candidates)] + (if candidates (if (empty? valids) (recur (inc i)) (if (empty? (first valids)) @@ -217,7 +218,8 @@ (attributes new-scale) (incidence-relation new-scale)) (comp comp-scale-image (measure sm)))) - (map #(into init-cluster %) valids)))))) + (map #(into init-cluster %) valids))) + nil)))) (defmulti cluster "Clusters attributes or objects in the scale context. @@ -284,12 +286,14 @@ "This is a wrapper method to flatten the cluster result." [kind quant sm thing] (let [result (cluster kind quant sm thing)] - (if (coll? result) - (map (partial reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) #{}) - result) - (rename-scale kind result (fn [k] - (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) - #{} k)))))) + (if result + (if (coll? result) + (map (partial reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) #{}) + result) + (rename-scale kind result (fn [k] + (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) + #{} k)))) + nil))) (defmulti repair-cluster "Given a scale context constructs a valid smeasure scale by using as @@ -298,7 +302,7 @@ (fn [quantifier & args] quantifier)) (alter-meta! #'repair-cluster assoc :private true) -(defmethod repair-cluster :all ;; todo stackoverflow +(defmethod repair-cluster :all [_ ctx s] (loop [broken-scale s] (let [br-exts (extents broken-scale) @@ -316,6 +320,23 @@ (recur (apply-flattened-cluster fixed-extent))) broken-scale)))) +(defmethod repair-cluster :ex + [_ ctx s] + (loop [broken-scale s] + (let [br-exts (extents broken-scale) + pre-images (sort-by count + (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat + br-exts)) + not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] + (if (= orig-e e) nil orig-e))) + image (fn [o] (some + #(if (contains? % o) % false) (objects broken-scale))) + broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality + (if broken + (let [apply-flattened-cluster (flattened-cluster-applier broken-scale :objects :ex) + fixed-extent (reduce conj #{} (map image broken))] + (recur (apply-flattened-cluster fixed-extent))) + broken-scale)))) ;; (defmethod repair-cluster :ex ;; [_ ctx broken-scale] ;; TODO) @@ -409,8 +430,8 @@ (:attr-cl-quantifier args) (:obj-cl-quantifier args)) candidates (if (= :objects kind) - (map set (take 3 (partition 2 (shuffle (objects scale-ctx))))) - (map set (take 3 (partition 2 (shuffle (attributes scale-ctx)))))) + (map set (take 5 (partition 2 (shuffle (objects scale-ctx))))) + (map set (take 5 (partition 2 (shuffle (attributes scale-ctx)))))) ;; how large the clusters get sm (make-smeasure-nc ctx scale-ctx (fn [o] @@ -421,13 +442,18 @@ (let [result (flattened-cluster kind quant sm thing)] - (if (coll? result) (count (first result)) - (apply + (map count thing))))) + (if result + (if (coll? result) (count (first result)) + (apply + (map count thing))) + Integer/MAX_VALUE))) smallest (apply min-key key-fkt candidates) flat-clustered (cluster kind quant sm smallest)] - (if (coll? flat-clustered) ;;clustering was not valid, but returned a list of valid superclusters - (scale (flattened-cluster kind quant sm (first flat-clustered))) - (scale (flattened-cluster kind quant sm smallest))))) + (if flat-clustered + (if (coll? flat-clustered) ;;clustering was not valid, but returned a list of valid superclusters + (scale (flattened-cluster kind quant sm (first flat-clustered))) + (scale (flattened-cluster kind quant sm smallest))) + (make-context #{(set (objects ctx))} #{(set (attributes ctx))} + #{[#{(set (objects ctx))} #{(set (attributes ctx))}]})))) ;TODO fix incidence (defn- fill-individual-cluster "Inserts as many objects/attributes to the individual as possible. @@ -435,7 +461,7 @@ [args ctx {iobjs :objects iattr :attributes :as ind}] (let [repaired-ind (->> ind (ind2clustered-ctx args ctx) - (repair-cluster :all ctx)) + (repair-cluster (:obj-cl-quantifier args) ctx)) make-ind-map #(hash-map :objects (objects %) :attributes (attributes %)) context2d? (comp la/bipartite? incompatibility-graph)] (loop [tmp-ind repaired-ind] ;; apply small clusters until 2D @@ -614,7 +640,7 @@ (->> (concat pairing (repeat (rand-pair))) (take (- (:generation-size args) (:survival-count args))) (into []) - (map (fn [[ind1 ind2]] (breeding-cluster args ctx ind1 ind2)))))))) + (pmap (fn [[ind1 ind2]] (breeding-cluster args ctx ind1 ind2)))))))) (defn- next-generation "Given the current generation of contexts, breeds the next generation." @@ -641,9 +667,10 @@ at most two." [args ctx] (into [] - (for [i (range (:generation-size args))] - (fill-individual-cluster args ctx - ((:init-cluster args) ctx))))) + (pmap (fn [i] + (fill-individual-cluster args ctx + ((:init-cluster args) ctx))) + (range (:generation-size args))))) (defn- first-generation "Computes a first random generation of contexts with order dimension From 90e840943d66b1b01471b90582fd236a0b3f6df0 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 26 May 2020 13:35:35 +0200 Subject: [PATCH 030/117] genetic part 1 works now --- src/main/clojure/conexp/fca/smeasure.clj | 294 ++++++++++++++--------- 1 file changed, 180 insertions(+), 114 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 3e873f7f4..6b2c9865d 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -13,9 +13,13 @@ [conexp.fca.cover :refer [generate-concept-cover]] [clojure.math.combinatorics :as comb] [loom.graph :as lg] - [loom.alg :as la]) + [loom.alg :as la] + [clojure.core.reducers :as :r]) (:import [org.dimdraw Bipartite])) +(require '[taoensso.tufte :as tufte :refer (defnp p profiled profile)]) +(tufte/add-basic-println-handler! {}) + (defprotocol Smeasure (context [sm] "Returns the original context that is measured.") (scale [sm] "Returns the scale that measures the context.") @@ -132,7 +136,7 @@ ext (get-exts original)] (fn [clustered-scale pre-image] (let [ext-new (get-exts (transform-bv-cover scale clustered-scale original))] - (subset? (set (map pre-image ext-new)) ext))))) + (subset? (set (map pre-image) ext-new) ext))))) (defmulti cluster-applier "Clusters attributes or objects in the scale context. @@ -199,7 +203,7 @@ (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) #{} a)))))) -(defn- cluster-until-valid +(defnp cluster-until-valid "This is a helper method, that applies a certain clustering until a valid scale measure is outputted. If not unique, returns a seq of valid candidates." @@ -244,12 +248,13 @@ apply-cluster (cluster-applier :attributes :ex s) original (generate-concept-cover (concepts s)) comp-scale-image identity - scale-pre-image identity - valid-cluster? (valid-cluster s original) + scale-pre-image (constantly identity) + ;valid-cluster? (valid-cluster s original) - valid-cluster? (fn [additional-attr] ((valid-cluster s original) - (apply-cluster (into attr additional-attr)) - (scale-pre-image (into attr additional-attr)))) + valid-cluster? (fn [additional-attr] (if ((valid-cluster s original) + (apply-cluster (into attr additional-attr)) + (scale-pre-image (into attr additional-attr))) + additional-attr false)) build-candidates (fn [i] (comb/combinations (seq (difference (attributes s) attr)) i))] (cluster-until-valid sm attr apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))) @@ -261,9 +266,10 @@ original (generate-concept-cover (concepts s)) comp-scale-image (fn [g] (if (contains? obj g) obj g)) scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) - valid-cluster? (fn [additional-obj] ((valid-cluster s original) - (apply-cluster (into obj additional-obj)) - (scale-pre-image (into obj additional-obj)))) + valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) + (apply-cluster (into obj additional-obj)) + (scale-pre-image (into obj additional-obj))) + additional-obj false)) build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] (cluster-until-valid sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))) @@ -275,9 +281,10 @@ original (generate-concept-cover (concepts s)) comp-scale-image (fn [g] (if (contains? obj g) obj g)) scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) - valid-cluster? (fn [additional-obj] ((valid-cluster s original) - (apply-cluster (into obj additional-obj)) - (scale-pre-image (into obj additional-obj)))) + valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) + (apply-cluster (into obj additional-obj)) + (scale-pre-image (into obj additional-obj))) + additional-obj false)) build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] (cluster-until-valid sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))) @@ -299,29 +306,15 @@ "Given a scale context constructs a valid smeasure scale by using as few cluster methods as possible. 'quantifier specifies the cluster quantifier used by the clustering methods." - (fn [quantifier & args] quantifier)) + (fn [kind quantifier & args] [kind quantifier])) (alter-meta! #'repair-cluster assoc :private true) -(defmethod repair-cluster :all - [_ ctx s] - (loop [broken-scale s] - (let [br-exts (extents broken-scale) - pre-images (sort-by count - (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat - br-exts)) - not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] - (if (= orig-e e) nil orig-e))) - image (fn [o] (some - #(if (contains? % o) % false) (objects broken-scale))) - broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality - (if broken - (let [apply-flattened-cluster (flattened-cluster-applier broken-scale :objects :all) - fixed-extent (reduce conj #{} (map image broken))] - (recur (apply-flattened-cluster fixed-extent))) - broken-scale)))) +(defmethod repair-cluster [:attributes :all] + [_ _ ctx s] + s) ;; attribute :all clusters are always valid -(defmethod repair-cluster :ex - [_ ctx s] +(defmethod repair-cluster [:objects :all] + [_ _ ctx s] (loop [broken-scale s] (let [br-exts (extents broken-scale) pre-images (sort-by count @@ -329,19 +322,64 @@ br-exts)) not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] (if (= orig-e e) nil orig-e))) +; not-closedd? (fn [e] (let [orig-e (context-object-closure ctx e)] + ; (if (= orig-e e) nil e))) image (fn [o] (some #(if (contains? % o) % false) (objects broken-scale))) - broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality + broken (some not-closed? pre-images) + ;; old (some not-closedd? pre-images) + ;; o (println broken-scale "\n" broken old) + ] ; returns first non extent of lowest cardinality (if broken - (let [apply-flattened-cluster (flattened-cluster-applier broken-scale :objects :ex) + (let [;o (println "entered" broken) + apply-flattened-cluster (flattened-cluster-applier broken-scale :objects :all) fixed-extent (reduce conj #{} (map image broken))] (recur (apply-flattened-cluster fixed-extent))) - broken-scale)))) -;; (defmethod repair-cluster :ex -;; [_ ctx broken-scale] -;; TODO) + ;(do (println "entered " s "\n returned" broken-scale) + broken-scale + ; ) + )))) -(defn- incompatibility-graph +(defmethod repair-cluster [:objects :ex] + [_ _ ctx s] + (loop [broken-scale s] + (if (-> s attributes count (= 1)) (repair-cluster :attributes :ex ctx broken-scale) + (let [br-exts (extents broken-scale) + pre-images (sort-by count + (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat + br-exts)) + not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] + (if (= orig-e e) nil orig-e))) + image (fn [o] (some + #(if (contains? % o) % false) (objects broken-scale))) + broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality + (if broken + (let [apply-flattened-cluster (flattened-cluster-applier broken-scale :objects :ex) + fixed-extent (reduce conj #{} (map image broken))] + (recur (apply-flattened-cluster fixed-extent))) + broken-scale))))) + +(defmethod repair-cluster [:attributes :ex] + [_ _ ctx s] + (loop [broken-scale s] + (if (-> s attributes count (= 1)) (repair-cluster :objects :ex ctx broken-scale) + (let [br-exts (extents broken-scale) + pre-images (sort-by count + (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat + br-exts)) + not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] + (if (= orig-e e) nil orig-e))) + image (fn [o] (some + #(if (contains? % o) % false) (objects broken-scale))) + broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality + (if broken + (let [apply-flattened-cluster (flattened-cluster-applier broken-scale :attributes :ex) + fixed-intent (object-derivation s (reduce conj #{} (map image broken)))] + (recur (apply-flattened-cluster fixed-intent))) + broken-scale))))) + + +(defnp incompatibility-graph "For a formal context computes the imcompatibility graph of its incidence relation." [ctx] @@ -350,9 +388,20 @@ incompatible? (fn [[[g m] [h n]]] (and ((incidence ctx) [g n]) ((incidence ctx) [h m]))) - edges (filter incompatible? (cross-product nodes nodes))] + edges (r/foldcat (r/filter incompatible? (cross-product nodes nodes)))] (apply lg/graph edges))) +(defn- updated-incompatibility-graph + [graph scale] + (let [new-nodes (difference (cross-product (objects scale) (attributes scale)) + (incidence-relation scale)) + sub (lg/subgraph graph (intersection (lg/nodes graph) new-nodes)) + + incompatible? (fn [[[g m] [h n]]] + (and ((incidence scale) [g n]) + ((incidence scale) [h m]))) + new-edges (filter incompatible? (cross-product (difference new-nodes (lg/nodes graph)) new-nodes))] + (apply lg/add-edges sub new-edges))) (defmulti add-if-bipartite "For a bipartite incompatibility graph of a subset of attributes @@ -416,8 +465,8 @@ (defn- ind2clustered-ctx "This is a helper method to apply the by the individual specified clustering." [args ctx {iobjs :objects iattr :attributes :as ind}] - (let [apply-cluster-obj (fn [tocluster-ctx cl] ((cluster-applier :objects (:obj-cl-quantifier args) tocluster-ctx) cl)) - apply-cluster-attr (fn [tocluster-ctx cl] ((cluster-applier :attributes (:attr-cl-quantifier args) tocluster-ctx) cl))] + (let [apply-cluster-obj (fn [tocluster-ctx cl] ((cluster-applier :objects (:quant args) tocluster-ctx) cl)) + apply-cluster-attr (fn [tocluster-ctx cl] ((cluster-applier :attributes (:quant args) tocluster-ctx) cl))] (reduce apply-cluster-obj (reduce apply-cluster-attr ctx iattr) iobjs))) @@ -425,49 +474,61 @@ "This is a helper method to apply the smallest clustering out of a few random valid clusterings." [args ctx scale-ctx] - (let [kind (rand-nth [:attributes :objects]) - quant (if (= :attributes kind) - (:attr-cl-quantifier args) - (:obj-cl-quantifier args)) - candidates (if (= :objects kind) - (map set (take 5 (partition 2 (shuffle (objects scale-ctx))))) - (map set (take 5 (partition 2 (shuffle (attributes scale-ctx)))))) + (let [kind (rand-nth [:attributes :objects]) + quant (:quant args) + candidates (if (and (= :objects kind) (-> scale-ctx objects count (= 1) not)) + (take 10 (partition 2 (shuffle (objects scale-ctx)))) + (take 10 (partition 2 (shuffle (attributes scale-ctx))))) + apply-flattened-cluster (flattened-cluster-applier scale-ctx kind quant) + + derivation-op (if (= kind :objects) object-derivation attribute-derivation) + key-fkt (fn [[a b]] (let [da (derivation-op scale-ctx #{a}) + db (derivation-op scale-ctx #{b})] + (+ (count (difference da db)) + (count (difference db da))))) + most-in-common (apply min-key key-fkt candidates) + smallest (repair-cluster kind quant ctx (apply-flattened-cluster (set most-in-common))) + ;; how large the clusters get - sm (make-smeasure-nc ctx scale-ctx - (fn [o] - (some - #(if (contains? % o) % false) - (objects scale-ctx)))) - key-fkt (fn [thing] - (let [result (flattened-cluster kind - quant - sm thing)] - (if result - (if (coll? result) (count (first result)) - (apply + (map count thing))) - Integer/MAX_VALUE))) - smallest (apply min-key key-fkt candidates) - flat-clustered (cluster kind quant sm smallest)] - (if flat-clustered - (if (coll? flat-clustered) ;;clustering was not valid, but returned a list of valid superclusters - (scale (flattened-cluster kind quant sm (first flat-clustered))) - (scale (flattened-cluster kind quant sm smallest))) - (make-context #{(set (objects ctx))} #{(set (attributes ctx))} - #{[#{(set (objects ctx))} #{(set (attributes ctx))}]})))) ;TODO fix incidence + ;; sm (make-smeasure-nc ctx scale-ctx + ;; (fn [o] + ;; (some + ;; #(if (contains? % o) % false) + ;; (objects scale-ctx)))) + + ;; applied-candidates (map (fn [thing] (repair-cluster kind quant ctx (apply-flattened-cluster thing))) candidates) + + ;; smallest (apply min-key (fn [result] + ;; (if result + ;; (count (objects result)) + ;; Integer/MAX_VALUE)) applied-candidates) + ] + (if smallest smallest + (make-context #{(set (objects ctx))} #{(set (attributes ctx))} + #{[#{(set (objects ctx))} #{(set (attributes ctx))}]})))) ;TODO fix incidence + +(defnp ctx2d [g] + (la/bipartite? g)) + (defn- fill-individual-cluster "Inserts as many objects/attributes to the individual as possible. An individual is a set of nodes of the contexts incompatibility graph." - [args ctx {iobjs :objects iattr :attributes :as ind}] - (let [repaired-ind (->> ind - (ind2clustered-ctx args ctx) - (repair-cluster (:obj-cl-quantifier args) ctx)) + [args ctx graph {iobjs :objects iattr :attributes :as ind}] + (let [repair-kind (if (= (:quant args) :ex) + (rand-nth [:attributes :objects]) :objects) + repaired-ind (->> ind + (ind2clustered-ctx args ctx) + (repair-cluster repair-kind (:quant args) ctx)) make-ind-map #(hash-map :objects (objects %) :attributes (attributes %)) - context2d? (comp la/bipartite? incompatibility-graph)] - (loop [tmp-ind repaired-ind] ;; apply small clusters until 2D - (if (context2d? tmp-ind) + new-graph (updated-incompatibility-graph graph repaired-ind) + context2d? (comp la/bipartite? (partial updated-incompatibility-graph new-graph))] + (loop [tmp-ind repaired-ind g new-graph] ;; apply small clusters until 2D + (if (ctx2d g) (make-ind-map tmp-ind) - (recur (apply-small-rand-cluster args ctx tmp-ind)))))) + (let [new-ind (apply-small-rand-cluster args ctx tmp-ind) + new-g (updated-incompatibility-graph g new-ind)] + (recur new-ind new-g)))))) (defn- fill-individual "Inserts as many objects/attributes to the individual as possible. @@ -493,11 +554,10 @@ (defn- make-args-map "Returns default args updated by user input." [args] - (let [default-args {:generation-size 30 :generations 10 - :survival-ratio 0.1 :mutation-rate 0.3 + (let [default-args {:generation-size 10 :generations 10 + :survival-ratio 0.3 :mutation-rate 0.3 :fresh-chance 0.05 :mode :incidence-clustered - :obj-cl-quantifier :all - :attr-cl-quantifier :all + :quant :all :init {:objects #{} :attributes #{}} :init-cluster (fn [ctx] {:objects (reduce #(conj %1 #{%2}) #{} (objects ctx)) @@ -576,18 +636,18 @@ (defn- mutation-cluster "Mutates the current individual by removing an object or attribute given a probability." - [args ctx {iobjs :objects iattr :attributes :as ind}] - (if (> (:fresh-chance args) (rand)) - (fill-individual-cluster args ctx ((:init-cluster args) ctx)) - (let [mutated-obj (into #{} (random-sample (:mutation-rate args) iobjs)) - mutated-attr (into #{} (random-sample (:mutation-rate args) iattr))] - (-> ind - (assoc :objects (reduce (fn [ind-objs tomutate-obj-cl] ;; flattens the to mutate cluster #{1 2 3} -> #{1} #{2} #{3} - (reduce #(conj %1 #{%2}) ind-objs tomutate-obj-cl)) - (difference (:objects ind) mutated-obj) mutated-obj)) - (assoc :attributes (reduce (fn [ind-attr tomutate-attr-cl] - (reduce #(conj %1 #{%2}) ind-attr tomutate-attr-cl)) - (difference (:attributes ind) mutated-attr) mutated-attr)))))) + [args ctx graph {iobjs :objects iattr :attributes :as ind}] + ;; (if (> (:fresh-chance args) (rand)) + ;; (fill-individual-cluster args ctx graph ((:init-cluster args) ctx))) + (let [mutated-obj (into #{} (random-sample (:mutation-rate args) iobjs)) + mutated-attr (into #{} (random-sample (:mutation-rate args) iattr))] + (-> ind + (assoc :objects (reduce (fn [ind-objs tomutate-obj-cl] ;; flattens the to mutate cluster #{1 2 3} -> #{1} #{2} #{3} + (reduce #(conj %1 #{%2}) ind-objs tomutate-obj-cl)) + (difference (:objects ind) mutated-obj) mutated-obj)) + (assoc :attributes (reduce (fn [ind-attr tomutate-attr-cl] + (reduce #(conj %1 #{%2}) ind-attr tomutate-attr-cl)) + (difference (:attributes ind) mutated-attr) mutated-attr))))) (defn- mutation "Mutates the current individual by removing an object or attribute @@ -606,10 +666,10 @@ first computing the context of common attributes and objects. Secondly as many attributes/objects of ctx are inserted without increasing the order dimension of the new individual." - [args ctx ind1 ind2] - (->> (cluster-ind-intersecter ind1 ind2) - (mutation-cluster args ctx) - (fill-individual-cluster args ctx))) + [args ctx graph ind1 ind2] + (->> (cluster-ind-intersecter ind1 ind2) + (mutation-cluster args ctx graph) + (fill-individual-cluster args ctx graph))) (defn- breeding "Given two individuals, i.e. contexts, breeds a next new individual by @@ -622,13 +682,12 @@ (mutation args ctx graph) (fill-individual ctx graph))) -(defn- next-generation-cluster +(defnp next-generation-cluster "Given the current generation of contexts, breeds the next generation." - [args ctx generation] - (let [fitness-vals (->> generation - (sort-by (partial fitness args ctx)) + [args ctx graph generation] + (let [survivals (->> generation + (sort-by (partial fitness args ctx) >) (take (:survival-count args))) - survivals (take (:survival-count args) fitness-vals) pairing (->> survivals shuffle (partition 2)) @@ -640,7 +699,7 @@ (->> (concat pairing (repeat (rand-pair))) (take (- (:generation-size args) (:survival-count args))) (into []) - (pmap (fn [[ind1 ind2]] (breeding-cluster args ctx ind1 ind2)))))))) + (pmap (fn [[ind1 ind2]] (breeding-cluster args ctx graph ind1 ind2)))))))) (defn- next-generation "Given the current generation of contexts, breeds the next generation." @@ -662,14 +721,13 @@ (into []) (map #(apply breeding args ctx graph %))))))) -(defn- first-generation-cluster +(defnp first-generation-cluster "Computes a first random generation of contexts with order dimension at most two." - [args ctx] + [args ctx init-ctx graph] (into [] (pmap (fn [i] - (fill-individual-cluster args ctx - ((:init-cluster args) ctx))) + (fill-individual-cluster args ctx graph init-ctx)) (range (:generation-size args))))) (defn- first-generation @@ -682,20 +740,22 @@ (:init args))))) -(defn genetic-2d-cluster +(defnp genetic-2d-cluster "Genetic algorithm to determine a maximal sub-context with order dimension at most two. Maximal in terms of number of objects times number of attributes." [ctx & [args]] - (let [args (make-args-map (if (nil? args) {} args))] + (let [args (make-args-map (if (nil? args) {} args)) + init-ind ((:init-cluster args) ctx) + graph (incompatibility-graph (ind2clustered-ctx args ctx init-ind))] (loop [n (:generations args) - generation (first-generation-cluster args ctx)] + generation (first-generation-cluster args ctx init-ind graph)] (println "Generation: " (- (:generations args) n)) (if (= n 0) (->> generation (apply max-key (partial fitness args ctx)) (ind2clustered-ctx args ctx)) - (recur (dec n) (next-generation-cluster args ctx generation)))))) + (recur (dec n) (next-generation-cluster args ctx graph generation)))))) (defn genetic-2d-subctx "Genetic algorithm to determine a maximal sub-context with order @@ -950,3 +1010,9 @@ (recur evaluated))))) + +; (def c (profile {:dynamic? true} (genetic-2d-cluster bj {:generation-size 30 :generations 2 :quant :all}))) + +; (require '[conexp.io.contexts :refer :all]) + +; (def bj (read-context "../data/bj.ctx")) From 47d61f270d946a8066c14e4cba5675e80a99bc74 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 26 May 2020 14:21:50 +0200 Subject: [PATCH 031/117] genetic works Part 2 --- src/main/clojure/conexp/fca/smeasure.clj | 99 +++++++++--------------- 1 file changed, 35 insertions(+), 64 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 6b2c9865d..99f6574b1 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -14,7 +14,7 @@ [clojure.math.combinatorics :as comb] [loom.graph :as lg] [loom.alg :as la] - [clojure.core.reducers :as :r]) + [clojure.core.reducers :as r]) (:import [org.dimdraw Bipartite])) (require '[taoensso.tufte :as tufte :refer (defnp p profiled profile)]) @@ -306,15 +306,11 @@ "Given a scale context constructs a valid smeasure scale by using as few cluster methods as possible. 'quantifier specifies the cluster quantifier used by the clustering methods." - (fn [kind quantifier & args] [kind quantifier])) + (fn [quantifier & args] quantifier)) (alter-meta! #'repair-cluster assoc :private true) -(defmethod repair-cluster [:attributes :all] - [_ _ ctx s] - s) ;; attribute :all clusters are always valid - -(defmethod repair-cluster [:objects :all] - [_ _ ctx s] +(defmethod repair-cluster :all + [_ ctx s] (loop [broken-scale s] (let [br-exts (extents broken-scale) pre-images (sort-by count @@ -322,61 +318,38 @@ br-exts)) not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] (if (= orig-e e) nil orig-e))) -; not-closedd? (fn [e] (let [orig-e (context-object-closure ctx e)] - ; (if (= orig-e e) nil e))) image (fn [o] (some #(if (contains? % o) % false) (objects broken-scale))) - broken (some not-closed? pre-images) - ;; old (some not-closedd? pre-images) - ;; o (println broken-scale "\n" broken old) - ] ; returns first non extent of lowest cardinality + broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality (if broken - (let [;o (println "entered" broken) - apply-flattened-cluster (flattened-cluster-applier broken-scale :objects :all) - fixed-extent (reduce conj #{} (map image broken))] - (recur (apply-flattened-cluster fixed-extent))) - ;(do (println "entered " s "\n returned" broken-scale) - broken-scale - ; ) - )))) - -(defmethod repair-cluster [:objects :ex] - [_ _ ctx s] - (loop [broken-scale s] - (if (-> s attributes count (= 1)) (repair-cluster :attributes :ex ctx broken-scale) - (let [br-exts (extents broken-scale) - pre-images (sort-by count - (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat - br-exts)) - not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] - (if (= orig-e e) nil orig-e))) - image (fn [o] (some - #(if (contains? % o) % false) (objects broken-scale))) - broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality - (if broken - (let [apply-flattened-cluster (flattened-cluster-applier broken-scale :objects :ex) - fixed-extent (reduce conj #{} (map image broken))] - (recur (apply-flattened-cluster fixed-extent))) - broken-scale))))) - -(defmethod repair-cluster [:attributes :ex] - [_ _ ctx s] + (let [fixed-intent (object-derivation s (reduce conj #{} (map image broken))) + fixed-extent (reduce conj #{} (map image broken)) + [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 + (sort-by (comp count second) [[:objects fixed-extent] [:attributes fixed-intent]]))) + apply-flattened-cluster (flattened-cluster-applier broken-scale kind :all)] + (recur (apply-flattened-cluster fixed-cluster))) + broken-scale)))) + +(defmethod repair-cluster :ex + [_ ctx s] (loop [broken-scale s] - (if (-> s attributes count (= 1)) (repair-cluster :objects :ex ctx broken-scale) - (let [br-exts (extents broken-scale) - pre-images (sort-by count - (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat - br-exts)) - not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] - (if (= orig-e e) nil orig-e))) - image (fn [o] (some - #(if (contains? % o) % false) (objects broken-scale))) - broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality - (if broken - (let [apply-flattened-cluster (flattened-cluster-applier broken-scale :attributes :ex) - fixed-intent (object-derivation s (reduce conj #{} (map image broken)))] - (recur (apply-flattened-cluster fixed-intent))) - broken-scale))))) + (let [br-exts (extents broken-scale) + pre-images (sort-by count + (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat + br-exts)) + not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] + (if (= orig-e e) nil orig-e))) + image (fn [o] (some + #(if (contains? % o) % false) (objects broken-scale))) + broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality + (if broken + (let [fixed-intent (object-derivation s (reduce conj #{} (map image broken))) + fixed-extent (reduce conj #{} (map image broken)) + [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 + (sort-by (comp count second) [[:objects fixed-extent] [:attributes fixed-intent]]))) + apply-flattened-cluster (flattened-cluster-applier broken-scale kind :ex)] + (recur (apply-flattened-cluster fixed-cluster))) + broken-scale)))) (defnp incompatibility-graph @@ -487,7 +460,7 @@ (+ (count (difference da db)) (count (difference db da))))) most-in-common (apply min-key key-fkt candidates) - smallest (repair-cluster kind quant ctx (apply-flattened-cluster (set most-in-common))) + smallest (repair-cluster quant ctx (apply-flattened-cluster (set most-in-common))) ;; how large the clusters get ;; sm (make-smeasure-nc ctx scale-ctx @@ -515,11 +488,9 @@ "Inserts as many objects/attributes to the individual as possible. An individual is a set of nodes of the contexts incompatibility graph." [args ctx graph {iobjs :objects iattr :attributes :as ind}] - (let [repair-kind (if (= (:quant args) :ex) - (rand-nth [:attributes :objects]) :objects) - repaired-ind (->> ind + (let [repaired-ind (->> ind (ind2clustered-ctx args ctx) - (repair-cluster repair-kind (:quant args) ctx)) + (repair-cluster (:quant args) ctx)) make-ind-map #(hash-map :objects (objects %) :attributes (attributes %)) new-graph (updated-incompatibility-graph graph repaired-ind) context2d? (comp la/bipartite? (partial updated-incompatibility-graph new-graph))] From cdd4a2a7c87f5caae89d4ce39a274e0dfc95d63f Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 26 May 2020 15:27:33 +0200 Subject: [PATCH 032/117] Code Refactoring --- src/main/clojure/conexp/fca/smeasure.clj | 452 ++++++----------------- 1 file changed, 120 insertions(+), 332 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 99f6574b1..f85394fea 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -17,9 +17,6 @@ [clojure.core.reducers :as r]) (:import [org.dimdraw Bipartite])) -(require '[taoensso.tufte :as tufte :refer (defnp p profiled profile)]) -(tufte/add-basic-println-handler! {}) - (defprotocol Smeasure (context [sm] "Returns the original context that is measured.") (scale [sm] "Returns the scale that measures the context.") @@ -203,7 +200,56 @@ (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) #{} a)))))) -(defnp cluster-until-valid +(defmulti repair-cluster + "Given a scale context constructs a valid smeasure scale by using as + few cluster methods as possible. 'quantifier specifies the cluster + quantifier used by the clustering methods." + (fn [quantifier & args] quantifier)) +(alter-meta! #'repair-cluster assoc :private true) + +(defmethod repair-cluster :all + [_ ctx s] + (loop [broken-scale s] + (let [br-exts (extents broken-scale) + pre-images (sort-by count + (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat + br-exts)) + not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] + (if (= orig-e e) nil orig-e))) + image (fn [o] (some + #(if (contains? % o) % false) (objects broken-scale))) + broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality + (if broken + (let [fixed-intent (object-derivation s (reduce conj #{} (map image broken))) + fixed-extent (reduce conj #{} (map image broken)) + [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 + (sort-by (comp count second) [[:objects fixed-extent] [:attributes fixed-intent]]))) + apply-flattened-cluster (flattened-cluster-applier broken-scale kind :all)] + (recur (apply-flattened-cluster fixed-cluster))) + broken-scale)))) + +(defmethod repair-cluster :ex + [_ ctx s] + (loop [broken-scale s] + (let [br-exts (extents broken-scale) + pre-images (sort-by count + (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat + br-exts)) + not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] + (if (= orig-e e) nil orig-e))) + image (fn [o] (some + #(if (contains? % o) % false) (objects broken-scale))) + broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality + (if broken + (let [fixed-intent (object-derivation s (reduce conj #{} (map image broken))) + fixed-extent (reduce conj #{} (map image broken)) + [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 + (sort-by (comp count second) [[:objects fixed-extent] [:attributes fixed-intent]]))) + apply-flattened-cluster (flattened-cluster-applier broken-scale kind :ex)] + (recur (apply-flattened-cluster fixed-cluster))) + broken-scale)))) + +(defn- cluster-until-valid "This is a helper method, that applies a certain clustering until a valid scale measure is outputted. If not unique, returns a seq of valid candidates." @@ -243,51 +289,57 @@ (make-smeasure-nc (context sm) (apply-cluster attr) (measure sm)))) (defmethod cluster [:attributes :ex] - [_ _ sm attr] + [_ _ sm attr & [smart]] (let [s (scale sm) - apply-cluster (cluster-applier :attributes :ex s) - original (generate-concept-cover (concepts s)) - comp-scale-image identity - scale-pre-image (constantly identity) - ;valid-cluster? (valid-cluster s original) - - valid-cluster? (fn [additional-attr] (if ((valid-cluster s original) - (apply-cluster (into attr additional-attr)) - (scale-pre-image (into attr additional-attr))) - additional-attr false)) - build-candidates (fn [i] (comb/combinations (seq (difference (attributes s) attr)) i))] - (cluster-until-valid - sm attr apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))) - + apply-cluster (cluster-applier :attributes :ex s)] + (if smart + (repair-cluster :ex (context sm) (apply-cluster attr)) + (let [original (generate-concept-cover (concepts s)) + comp-scale-image identity + scale-pre-image (constantly identity) + ;valid-cluster? (valid-cluster s original) + + valid-cluster? (fn [additional-attr] (if ((valid-cluster s original) + (apply-cluster (into attr additional-attr)) + (scale-pre-image (into attr additional-attr))) + additional-attr false)) + build-candidates (fn [i] (comb/combinations (seq (difference (attributes s) attr)) i))] + (cluster-until-valid + sm attr apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))))) + (defmethod cluster [:objects :all] - [_ _ sm obj] + [_ _ sm obj & [smart]] (let [s (scale sm) - apply-cluster (cluster-applier :objects :all s) - original (generate-concept-cover (concepts s)) - comp-scale-image (fn [g] (if (contains? obj g) obj g)) - scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) - valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) - (apply-cluster (into obj additional-obj)) - (scale-pre-image (into obj additional-obj))) - additional-obj false)) - build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] - (cluster-until-valid - sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))) + apply-cluster (cluster-applier :objects :all s)] + (if smart + (repair-cluster :all (context sm) (apply-cluster obj)) + (let [original (generate-concept-cover (concepts s)) + comp-scale-image (fn [g] (if (contains? obj g) obj g)) + scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) + valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) + (apply-cluster (into obj additional-obj)) + (scale-pre-image (into obj additional-obj))) + additional-obj false)) + build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] + (cluster-until-valid + sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))))) (defmethod cluster [:objects :ex] - [_ _ sm obj] + [_ _ sm obj & [smart]] (let [s (scale sm) - apply-cluster (cluster-applier :objects :ex s) - original (generate-concept-cover (concepts s)) - comp-scale-image (fn [g] (if (contains? obj g) obj g)) - scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) - valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) - (apply-cluster (into obj additional-obj)) - (scale-pre-image (into obj additional-obj))) - additional-obj false)) - build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] - (cluster-until-valid - sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))) + apply-cluster (cluster-applier :objects :ex s)] + (if smart + (repair-cluster :all (context sm) (apply-cluster obj)) + (let [original (generate-concept-cover (concepts s)) + comp-scale-image (fn [g] (if (contains? obj g) obj g)) + scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) + valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) + (apply-cluster (into obj additional-obj)) + (scale-pre-image (into obj additional-obj))) + additional-obj false)) + build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] + (cluster-until-valid + sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))))) (defn- flattened-cluster "This is a wrapper method to flatten the cluster result." @@ -302,57 +354,7 @@ #{} k)))) nil))) -(defmulti repair-cluster - "Given a scale context constructs a valid smeasure scale by using as - few cluster methods as possible. 'quantifier specifies the cluster - quantifier used by the clustering methods." - (fn [quantifier & args] quantifier)) -(alter-meta! #'repair-cluster assoc :private true) - -(defmethod repair-cluster :all - [_ ctx s] - (loop [broken-scale s] - (let [br-exts (extents broken-scale) - pre-images (sort-by count - (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat - br-exts)) - not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] - (if (= orig-e e) nil orig-e))) - image (fn [o] (some - #(if (contains? % o) % false) (objects broken-scale))) - broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality - (if broken - (let [fixed-intent (object-derivation s (reduce conj #{} (map image broken))) - fixed-extent (reduce conj #{} (map image broken)) - [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 - (sort-by (comp count second) [[:objects fixed-extent] [:attributes fixed-intent]]))) - apply-flattened-cluster (flattened-cluster-applier broken-scale kind :all)] - (recur (apply-flattened-cluster fixed-cluster))) - broken-scale)))) - -(defmethod repair-cluster :ex - [_ ctx s] - (loop [broken-scale s] - (let [br-exts (extents broken-scale) - pre-images (sort-by count - (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat - br-exts)) - not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] - (if (= orig-e e) nil orig-e))) - image (fn [o] (some - #(if (contains? % o) % false) (objects broken-scale))) - broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality - (if broken - (let [fixed-intent (object-derivation s (reduce conj #{} (map image broken))) - fixed-extent (reduce conj #{} (map image broken)) - [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 - (sort-by (comp count second) [[:objects fixed-extent] [:attributes fixed-intent]]))) - apply-flattened-cluster (flattened-cluster-applier broken-scale kind :ex)] - (recur (apply-flattened-cluster fixed-cluster))) - broken-scale)))) - - -(defnp incompatibility-graph +(defn- incompatibility-graph "For a formal context computes the imcompatibility graph of its incidence relation." [ctx] @@ -376,45 +378,6 @@ new-edges (filter incompatible? (cross-product (difference new-nodes (lg/nodes graph)) new-nodes))] (apply lg/add-edges sub new-edges))) -(defmulti add-if-bipartite - "For a bipartite incompatibility graph of a subset of attributes - and objects of a context, computes if adding an object/attribute - preserves the bipartite property." - (fn [& args] (first args))) -(alter-meta! #'add-if-bipartite assoc :private true) - -(defmethod add-if-bipartite :object - [_ graph {iobjs :objects iattr :attributes :as ind} add-objs] - (let [old-nodes (into #{} - (filter #(and (contains? iattr (second %)) - (contains? iobjs (first %))) (lg/nodes graph))) - {new-objs :objects :as new-ind} (update ind :objects conj add-objs) - new-nodes (into #{} - (filter #(and (contains? new-objs (first %)) - (contains? iattr (second %))) (lg/nodes graph))) - ;; A node can be added if it is not in an odd cycle with itself - not-addable? (fn [n] - (. Bipartite isInOddCycle (:adj graph) (disj new-nodes n) n))] - (if (->> (difference new-nodes old-nodes) - (some not-addable?)) - ind new-ind))) - -(defmethod add-if-bipartite :attribute - [_ graph {iobjs :objects iattr :attributes :as ind} add-attr] - (let [old-nodes (into #{} - (filter #(and (contains? iattr (second %)) - (contains? iobjs (first %))) (lg/nodes graph))) - {new-attr :attributes :as new-ind} (update ind :attributes conj add-attr) - new-nodes (into #{} - (filter #(and (contains? new-attr (second %)) - (contains? iobjs (first %))) (lg/nodes graph))) - ;; A node can be added if it is not in an odd cycle with itself - not-addable? (fn [n] - (. Bipartite isInOddCycle (:adj graph) (disj new-nodes n) n))] - (if (->> (difference new-nodes old-nodes) - (some not-addable?)) - ind new-ind))) - (defn- cluster-ind-intersecter "This method computed the intersection between two cluster individuals by computing the splittance." [{iobjs1 :objects iattr1 :attributes :as ind1} @@ -460,31 +423,12 @@ (+ (count (difference da db)) (count (difference db da))))) most-in-common (apply min-key key-fkt candidates) - smallest (repair-cluster quant ctx (apply-flattened-cluster (set most-in-common))) - - ;; how large the clusters get - ;; sm (make-smeasure-nc ctx scale-ctx - ;; (fn [o] - ;; (some - ;; #(if (contains? % o) % false) - ;; (objects scale-ctx)))) - - ;; applied-candidates (map (fn [thing] (repair-cluster kind quant ctx (apply-flattened-cluster thing))) candidates) - - ;; smallest (apply min-key (fn [result] - ;; (if result - ;; (count (objects result)) - ;; Integer/MAX_VALUE)) applied-candidates) - ] + smallest (repair-cluster quant ctx (apply-flattened-cluster (set most-in-common)))] (if smallest smallest (make-context #{(set (objects ctx))} #{(set (attributes ctx))} #{[#{(set (objects ctx))} #{(set (attributes ctx))}]})))) ;TODO fix incidence -(defnp ctx2d [g] - (la/bipartite? g)) - - -(defn- fill-individual-cluster +(defn- fill-individual "Inserts as many objects/attributes to the individual as possible. An individual is a set of nodes of the contexts incompatibility graph." [args ctx graph {iobjs :objects iattr :attributes :as ind}] @@ -492,34 +436,14 @@ (ind2clustered-ctx args ctx) (repair-cluster (:quant args) ctx)) make-ind-map #(hash-map :objects (objects %) :attributes (attributes %)) - new-graph (updated-incompatibility-graph graph repaired-ind) - context2d? (comp la/bipartite? (partial updated-incompatibility-graph new-graph))] + new-graph (updated-incompatibility-graph graph repaired-ind)] (loop [tmp-ind repaired-ind g new-graph] ;; apply small clusters until 2D - (if (ctx2d g) + (if (la/bipartite? g) (make-ind-map tmp-ind) (let [new-ind (apply-small-rand-cluster args ctx tmp-ind) new-g (updated-incompatibility-graph g new-ind)] (recur new-ind new-g)))))) -(defn- fill-individual - "Inserts as many objects/attributes to the individual as possible. - An individual is a set of nodes of the contexts incompatibility graph." - [ctx graph {iobjs :objects iattr :attributes :as ind}] - (let [;; missing objects and attributes in the individual - tofill-obj (difference (objects ctx) iobjs) - tofill-attr (difference (attributes ctx) iattr) - tofill (into [] (concat (zip (repeat :attribute) tofill-attr) - (zip (repeat :object) tofill-obj))) - ;; add if addable - add-if-addable (fn [tmp-ind [kind toadd]] - (add-if-bipartite kind graph tmp-ind toadd))] - (->> tofill - shuffle - (reduce add-if-addable ind)))) - - - - ;;genetic algorithm (defn- make-args-map @@ -552,32 +476,12 @@ (fn [args & params] (:mode args))) (alter-meta! #'fitness assoc :private true) -(defmethod fitness :clustered - [_ & args] - (apply fitness :default args)) - -(defmethod fitness :concepts - [_ ctx {iobjs :objects iattr :attributes :as ind}] - (-> (make-context iobjs iattr (incidence ctx)) - concepts - count)) - (defmethod fitness :concepts-cluster [args ctx {iobjs :objects iattr :attributes :as ind}] (-> (ind2clustered-ctx args ctx ind) concepts count)) -(defmethod fitness :ctx-nontrivia - [_ ctx {iobjs :objects iattr :attributes :as ind}] - (let [sub-ctx (make-context iobjs iattr (incidence ctx)) - nontrivia-obj (filter #(not (empty? (object-derivation sub-ctx #{%}))) - (objects sub-ctx)) - nontrivia-attr (filter #(not (empty? (attribute-derivation sub-ctx #{%}))) - (attributes sub-ctx))] - (* (count nontrivia-obj) - (count nontrivia-attr)))) - (defmethod fitness :nontrivia-clustered [args ctx {iobjs :objects iattr :attributes :as ind}] (let [sub-ctx (ind2clustered-ctx args ctx ind) @@ -588,12 +492,6 @@ (* (count nontrivia-obj) (count nontrivia-attr)))) - -(defmethod fitness :incidence - [_ ctx {iobjs :objects iattr :attributes :as ind}] - (let [sub-ctx (make-context iobjs iattr (incidence ctx))] - (count (incidence-relation sub-ctx)))) - (defmethod fitness :incidence-clustered [args ctx {iobjs :objects iattr :attributes :as ind}] (let [sub-ctx (ind2clustered-ctx args ctx ind)] @@ -604,7 +502,7 @@ (* (count iobjs) (count iattr))) -(defn- mutation-cluster +(defn- mutation "Mutates the current individual by removing an object or attribute given a probability." [args ctx graph {iobjs :objects iattr :attributes :as ind}] @@ -620,40 +518,17 @@ (reduce #(conj %1 #{%2}) ind-attr tomutate-attr-cl)) (difference (:attributes ind) mutated-attr) mutated-attr))))) -(defn- mutation - "Mutates the current individual by removing an object or attribute - given a probability." - [args ctx graph {iobjs :objects iattr :attributes :as ind}] - (if (> (:fresh-chance args) (rand)) - (fill-individual ctx graph (:init args)) - (let [mutated-obj (into #{} (random-sample (- 1 (:mutation-rate args)) iobjs)) - mutated-attr (into #{} (random-sample (- 1 (:mutation-rate args)) iattr))] - (-> ind - (assoc :objects mutated-obj) - (assoc :attributes mutated-attr))))) - -(defn- breeding-cluster +(defn- breeding "Given two individuals, i.e. contexts, breeds a next new individual by first computing the context of common attributes and objects. Secondly as many attributes/objects of ctx are inserted without increasing the order dimension of the new individual." [args ctx graph ind1 ind2] (->> (cluster-ind-intersecter ind1 ind2) - (mutation-cluster args ctx graph) - (fill-individual-cluster args ctx graph))) - -(defn- breeding - "Given two individuals, i.e. contexts, breeds a next new individual by - first computing the context of common attributes and - objects. Secondly as many attributes/objects of ctx are inserted - without increasing the order dimension of the new individual." - [args ctx graph - {iobjs :objects iattr :attributes} {iobjs2 :objects iattr2 :attributes}] - (->> {:objects (intersection iobjs iobjs2) :attributes (intersection iattr iattr2)} (mutation args ctx graph) - (fill-individual ctx graph))) + (fill-individual args ctx graph))) -(defnp next-generation-cluster +(defn- next-generation "Given the current generation of contexts, breeds the next generation." [args ctx graph generation] (let [survivals (->> generation @@ -670,121 +545,42 @@ (->> (concat pairing (repeat (rand-pair))) (take (- (:generation-size args) (:survival-count args))) (into []) - (pmap (fn [[ind1 ind2]] (breeding-cluster args ctx graph ind1 ind2)))))))) - -(defn- next-generation - "Given the current generation of contexts, breeds the next generation." - [args ctx graph generation] - (let [fitness-vals (->> generation - (sort-by (partial fitness args ctx)) - (take (:survival-count args))) - survivals (take (:survival-count args) fitness-vals) - pairing (->> survivals - shuffle - (partition 2)) - rand-pair (fn [] (->> survivals - shuffle - (take 2)))] - (into [] - (concat survivals - (->> (concat pairing (repeat (rand-pair))) - (take (- (:generation-size args) (:survival-count args))) - (into []) - (map #(apply breeding args ctx graph %))))))) + (pmap (fn [[ind1 ind2]] (breeding args ctx graph ind1 ind2)))))))) -(defnp first-generation-cluster +(defn- first-generation "Computes a first random generation of contexts with order dimension at most two." [args ctx init-ctx graph] (into [] (pmap (fn [i] - (fill-individual-cluster args ctx graph init-ctx)) + (fill-individual args ctx graph init-ctx)) (range (:generation-size args))))) -(defn- first-generation - "Computes a first random generation of contexts with order dimension - at most two." - [args ctx graph] - (into [] - (for [i (range (:generation-size args))] - (fill-individual ctx graph - (:init args))))) - - -(defnp genetic-2d-cluster - "Genetic algorithm to determine a maximal sub-context with order - dimension at most two. Maximal in terms of number of objects times - number of attributes." +(defn- genetic-2d + "This Method is a genetic algorithm to determine a scale whichs + concept lattice is of order dimension 2D. The methods simulated by + this algorithm are cluster methods only and for comprehensibility we + use only one cluster variation (:all, :or) at a time. Further note + that nested clusters of the same type (:all, :ex) are equivalent to + their flattened correspondence. This method uses a genetic algorithm + that determines a large sub-context, i.e. the number of objects + times attributes, whichs concept lattice is of order dimension at + most two. After that missing attributes are combined with existing + objects, attributes such that they preserve the order dimension." [ctx & [args]] (let [args (make-args-map (if (nil? args) {} args)) init-ind ((:init-cluster args) ctx) graph (incompatibility-graph (ind2clustered-ctx args ctx init-ind))] (loop [n (:generations args) - generation (first-generation-cluster args ctx init-ind graph)] + generation (first-generation args ctx init-ind graph)] (println "Generation: " (- (:generations args) n)) (if (= n 0) (->> generation (apply max-key (partial fitness args ctx)) (ind2clustered-ctx args ctx)) - (recur (dec n) (next-generation-cluster args ctx graph generation)))))) - -(defn genetic-2d-subctx - "Genetic algorithm to determine a maximal sub-context with order - dimension at most two. Maximal in terms of number of objects times - number of attributes." - [ctx & [args]] - (let [args (make-args-map args) - graph (incompatibility-graph ctx) - ind2subctx (fn [{iobjs :objects iattr :attributes}] - (make-context iobjs iattr (incidence ctx)))] - (loop [n (:generations args) - generation (first-generation args ctx graph)] - (if (= n 0) - (->> generation - (apply max-key (partial fitness args ctx)) - ind2subctx) (recur (dec n) (next-generation args ctx graph generation)))))) -;; post processing -(defn- fit-rest - "This method is a helper method for suggest_2d and given a scale - context and an original context, fits as many missing - objects/attributes to the scale by clustering without increasing the order - dimension of the scale concept lattice." - [ctx scale] - scale - ; compute ferres covering - ; loop over attribtues/objects - ) - -;; Suggest Scale - -(defn suggest_2d - "This Method is a genetic algorithm to determine a scale whichs - concept lattice is of order dimension 2D. The methods simulated by - this algorithm are cluster methods only and for comprehensibility we - use only one cluster variation (:all, :or) at a time. Further note - that nested clusters of the same type (:all, :ex) are equivalent to - their flattened correspondence. This method uses a genetic algorithm - that determines a large sub-context, i.e. the number of objects - times attributes, whichs concept lattice is of order dimension at - most two. After that missing attributes are combined with existing - objects, attributes such that they preserve the order dimension." - [ctx] - ; first determine subcontext by genetic algorithm - ; second fill in all missing attributes objects - (-> ctx - genetic-2d-subctx - (fit-rest ctx))) - - -;; (defn- two-ferres-covering -;; "Given a formal context compute a covering of the incidence relation -;; by two ferres relations." -;; [ctx] - -;; ) ;;; Declare REPL commands (defmulti run-repl-command @@ -941,7 +737,7 @@ (define-repl-fn suggest "Suggests a scale with two dimensional concept lattice." - (let [suggestion (suggest_2d (context smeasure))] + (let [suggestion (genetic-2d (context smeasure))] (println suggestion) (if (= 1 (ask "Do you wish to continue with the suggested scale? 1: yes, 0: no:" #(read-string (str (read-line))) @@ -979,11 +775,3 @@ (if (:done evaluated) (:smeasure evaluated) (recur evaluated))))) - - - -; (def c (profile {:dynamic? true} (genetic-2d-cluster bj {:generation-size 30 :generations 2 :quant :all}))) - -; (require '[conexp.io.contexts :refer :all]) - -; (def bj (read-context "../data/bj.ctx")) From 8b6719cfe747d0ee3d15b8ae72552034f4433e1f Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 26 May 2020 15:50:48 +0200 Subject: [PATCH 033/117] smart cluster in explor. and decode for genetic --- src/main/clojure/conexp/fca/smeasure.clj | 54 ++++++++++++++++++------ 1 file changed, 40 insertions(+), 14 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index f85394fea..c30ff0550 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -200,6 +200,7 @@ (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) #{} a)))))) +; todo check if smast cluster works after ordinary cluster (defmulti repair-cluster "Given a scale context constructs a valid smeasure scale by using as few cluster methods as possible. 'quantifier specifies the cluster @@ -290,11 +291,18 @@ (defmethod cluster [:attributes :ex] [_ _ sm attr & [smart]] - (let [s (scale sm) - apply-cluster (cluster-applier :attributes :ex s)] + (let [s (scale sm)] (if smart - (repair-cluster :ex (context sm) (apply-cluster attr)) - (let [original (generate-concept-cover (concepts s)) + (let [encode (fn [ctx] (-> ctx + (rename-attributes (fn [a] #{a})) + (rename-objects (fn [b] #{b})))) + decode (fn [ctx] (-> ctx + (rename-attributes (fn [a] (if (< 1 (count a)) a (first a)))) + (rename-objects (fn [b] (if (< 1 (count b)) b (first b)))))) + apply-flattened-cluster (flattened-cluster-applier :attributes :ex (encode s))] + (decode (repair-cluster :all (context sm) (apply-flattened-cluster attr)))) + (let [apply-cluster (cluster-applier :attributes :ex s) + original (generate-concept-cover (concepts s)) comp-scale-image identity scale-pre-image (constantly identity) ;valid-cluster? (valid-cluster s original) @@ -309,11 +317,18 @@ (defmethod cluster [:objects :all] [_ _ sm obj & [smart]] - (let [s (scale sm) - apply-cluster (cluster-applier :objects :all s)] + (let [s (scale sm)] (if smart - (repair-cluster :all (context sm) (apply-cluster obj)) - (let [original (generate-concept-cover (concepts s)) + (let [encode (fn [ctx] (-> ctx + (rename-attributes (fn [a] #{a})) + (rename-objects (fn [b] #{b})))) + decode (fn [ctx] (-> ctx + (rename-attributes (fn [a] (if (< 1 (count a)) a (first a)))) + (rename-objects (fn [b] (if (< 1 (count b)) b (first b)))))) + apply-flattened-cluster (flattened-cluster-applier :objects :all (encode s))] + (decode (repair-cluster :all (context sm) (apply-flattened-cluster obj)))) + (let [apply-cluster (cluster-applier :objects :all s) + original (generate-concept-cover (concepts s)) comp-scale-image (fn [g] (if (contains? obj g) obj g)) scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) @@ -326,11 +341,18 @@ (defmethod cluster [:objects :ex] [_ _ sm obj & [smart]] - (let [s (scale sm) - apply-cluster (cluster-applier :objects :ex s)] + (let [s (scale sm)] (if smart - (repair-cluster :all (context sm) (apply-cluster obj)) - (let [original (generate-concept-cover (concepts s)) + (let [encode (fn [ctx] (-> ctx + (rename-attributes (fn [a] #{a})) + (rename-objects (fn [b] #{b})))) + decode (fn [ctx] (-> ctx + (rename-attributes (fn [a] (if (< 1 (count a)) a (first a)))) + (rename-objects (fn [b] (if (< 1 (count b)) b (first b)))))) + apply-flattened-cluster (flattened-cluster-applier :objects :ex (encode s))] + (decode (repair-cluster :all (context sm) (apply-flattened-cluster obj)))) + (let [apply-cluster (cluster-applier :objects :ex s) + original (generate-concept-cover (concepts s)) comp-scale-image (fn [g] (if (contains? obj g) obj g)) scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) @@ -570,14 +592,18 @@ [ctx & [args]] (let [args (make-args-map (if (nil? args) {} args)) init-ind ((:init-cluster args) ctx) - graph (incompatibility-graph (ind2clustered-ctx args ctx init-ind))] + graph (incompatibility-graph (ind2clustered-ctx args ctx init-ind)) + decode (fn [ctx] (-> ctx + (rename-attributes (fn [a] (if (< 1 (count a)) a (first a)))) + (rename-objects (fn [b] (if (< 1 (count b)) b (first b))))))] (loop [n (:generations args) generation (first-generation args ctx init-ind graph)] (println "Generation: " (- (:generations args) n)) (if (= n 0) (->> generation (apply max-key (partial fitness args ctx)) - (ind2clustered-ctx args ctx)) + (ind2clustered-ctx args ctx) + decode) (recur (dec n) (next-generation args ctx graph generation)))))) From a5add488a1a5ad6e0b03091890945aca7099eb3d Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Thu, 28 May 2020 19:04:25 +0200 Subject: [PATCH 034/117] Fixed and improved Cluster Repair Algorithm --- src/main/clojure/conexp/fca/smeasure.clj | 70 ++++++++---------------- 1 file changed, 24 insertions(+), 46 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index f2f373c9d..91467c3af 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -281,55 +281,33 @@ #{} a)))))) ; todo check if smast cluster works after ordinary cluster -(defmulti repair-cluster + +(defn- repair-cluster "Given a scale context constructs a valid smeasure scale by using as few cluster methods as possible. 'quantifier specifies the cluster quantifier used by the clustering methods." - (fn [quantifier & args] quantifier)) -(alter-meta! #'repair-cluster assoc :private true) - -(defmethod repair-cluster :all - [_ ctx s] - (loop [broken-scale s] - (let [br-exts (extents broken-scale) + [quant ctx s] + (loop [broken-scale s] + (let [br-exts (extents broken-scale) ;todo smallest ext and repair obj or largest and repair attr - pre-images (sort-by count - (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat - br-exts)) - not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] - (if (= orig-e e) nil orig-e))) - image (fn [o] (some - #(if (contains? % o) % false) (objects broken-scale))) - broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality - (if broken - (let [fixed-intent (object-derivation s (reduce conj #{} (map image broken))) - fixed-extent (reduce conj #{} (map image broken)) - [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 - (sort-by (comp count second) [[:objects fixed-extent] [:attributes fixed-intent]]))) - apply-flattened-cluster (flattened-cluster-applier broken-scale kind :all)] - (recur (apply-flattened-cluster fixed-cluster))) - broken-scale)))) - -(defmethod repair-cluster :ex - [_ ctx s] - (loop [broken-scale s] - (let [br-exts (extents broken-scale) - pre-images (sort-by count - (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat - br-exts)) - not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] - (if (= orig-e e) nil orig-e))) - image (fn [o] (some - #(if (contains? % o) % false) (objects broken-scale))) - broken (some not-closed? pre-images)] ; returns first non extent of lowest cardinality - (if broken - (let [fixed-intent (object-derivation s (reduce conj #{} (map image broken))) - fixed-extent (reduce conj #{} (map image broken)) - [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 - (sort-by (comp count second) [[:objects fixed-extent] [:attributes fixed-intent]]))) - apply-flattened-cluster (flattened-cluster-applier broken-scale kind :ex)] - (recur (apply-flattened-cluster fixed-cluster))) - broken-scale)))) + pre-images (sort-by count + (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat + br-exts)) + rev-pre-images (reverse pre-images) + not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] + (if (= orig-e e) nil orig-e))) + image (fn [o] (some + #(if (contains? % o) % false) (objects broken-scale))) + broken (some not-closed? pre-images); returns first non extent of lowest cardinality + rev-broken (if broken (some not-closed? rev-pre-images) nil)] + (if broken + (let [fixed-intent (object-derivation broken-scale (reduce conj #{} (map image rev-broken))) + fixed-extent (reduce conj #{} (map image broken)) + [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 + (sort-by (comp count second) [[:objects fixed-extent] [:attributes fixed-intent]]))) + apply-flattened-cluster (flattened-cluster-applier broken-scale kind quant)] + (recur (apply-flattened-cluster fixed-cluster))) + broken-scale)))) (defn- cluster-until-valid "This is a helper method, that applies a certain clustering until a @@ -635,7 +613,7 @@ "Given the current generation of contexts, breeds the next generation." [args ctx graph generation] (let [survivals (->> generation - (sort-by (partail fitness args ctx) >) ;; todo parallel fitness apply + (sort-by (partial fitness args ctx) >) ;; todo parallel fitness apply (take (:survival-count args))) pairing (->> survivals shuffle From 8a358d412d517169ba820e2bec76e4db63333b07 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Fri, 29 May 2020 14:35:59 +0200 Subject: [PATCH 035/117] bigfix --- src/main/clojure/conexp/fca/smeasure.clj | 24 +++++++++++++++++------- 1 file changed, 17 insertions(+), 7 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 91467c3af..0d34402aa 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -301,7 +301,12 @@ broken (some not-closed? pre-images); returns first non extent of lowest cardinality rev-broken (if broken (some not-closed? rev-pre-images) nil)] (if broken - (let [fixed-intent (object-derivation broken-scale (reduce conj #{} (map image rev-broken))) + (let [fixed-intent (if (= quant :all) + (object-derivation broken-scale (reduce conj #{} (map image rev-broken))) + (reduce into #{} + (map (partial object-derivation broken-scale) + (map (partial conj #{}) + (map image broken))))) ;; TODO need different derivation for :ex fixed-extent (reduce conj #{} (map image broken)) [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 (sort-by (comp count second) [[:objects fixed-extent] [:attributes fixed-intent]]))) @@ -491,7 +496,7 @@ "This is a helper method to apply the smallest clustering out of a few random valid clusterings." [args ctx scale-ctx] - (let [kind (rand-nth [:attributes :objects]) + (let [kind (rand-nth [:attributes :objects]) quant (:quant args) candidates (if (and (= :objects kind) (-> scale-ctx objects count (= 1) not)) (take 10 (partition 2 (shuffle (objects scale-ctx)))) @@ -557,13 +562,13 @@ (fn [args & params] (:mode args))) (alter-meta! #'fitness assoc :private true) -(defmethod fitness :concepts-cluster +(defmethod fitness :concepts [args ctx {iobjs :objects iattr :attributes :as ind}] (-> (ind2clustered-ctx args ctx ind) concepts count)) -(defmethod fitness :nontrivia-clustered +(defmethod fitness :nontrivia [args ctx {iobjs :objects iattr :attributes :as ind}] (let [sub-ctx (ind2clustered-ctx args ctx ind) nontrivia-obj (filter #(not (empty? (object-derivation sub-ctx #{%}))) @@ -573,7 +578,7 @@ (* (count nontrivia-obj) (count nontrivia-attr)))) -(defmethod fitness :incidence-clustered +(defmethod fitness :incidence [args ctx {iobjs :objects iattr :attributes :as ind}] (let [sub-ctx (ind2clustered-ctx args ctx ind)] (count (incidence-relation sub-ctx)))) @@ -654,7 +659,11 @@ graph (incompatibility-graph (ind2clustered-ctx args ctx init-ind)) decode (fn [ctx] (-> ctx (rename-attributes (fn [a] (if (< 1 (count a)) a (first a)))) - (rename-objects (fn [b] (if (< 1 (count b)) b (first b))))))] + (rename-objects (fn [b] (if (< 1 (count b)) b (first b)))))) + to-sm (fn [scale] (make-smeasure-nc ctx scale + (fn [g] (if (contains? (objects scale) g) g + (some (fn [o] (and (set? o) (contains? o g))) + (objects c))))))] (loop [n (:generations args) generation (first-generation args ctx init-ind graph)] (println "Generation: " (- (:generations args) n)) @@ -662,7 +671,8 @@ (->> generation (apply max-key (partial fitness args ctx)) (ind2clustered-ctx args ctx) - decode) + decode + to-sm) (recur (dec n) (next-generation args ctx graph generation)))))) From 20ee336b85e6c2e9bd66a5d125da0201cd723c4d Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 7 Jul 2020 12:07:04 +0200 Subject: [PATCH 036/117] Added Cluster Validity checkers --- .../clojure/conexp/fca/concept_transform.clj | 7 +- src/main/clojure/conexp/fca/smeasure.clj | 304 ++++++++++++------ src/main/clojure/conexp/io/smeasure.clj | 2 +- 3 files changed, 208 insertions(+), 105 deletions(-) diff --git a/src/main/clojure/conexp/fca/concept_transform.clj b/src/main/clojure/conexp/fca/concept_transform.clj index 429bc77c8..e127ac323 100644 --- a/src/main/clojure/conexp/fca/concept_transform.clj +++ b/src/main/clojure/conexp/fca/concept_transform.clj @@ -82,6 +82,11 @@ ;;; general transformer +(defn cover-to-concepts + "This method converts the cover structure back to the list of concepts." + [cover] + (map #(vec [% (get-in cover [% :extent])]) (keys cover))) + (defn transform-bv "Transforms the set of concepts of ctx1 to that of ctx2 using the algorithm presented in 'Knowledge Cores in Large Formal Contexts' @@ -94,5 +99,5 @@ [ctx1 ctx2 concepts1] (let [bv1 (generate-concept-cover concepts1) bv2 (dual-concept-cover (transform-bv-cover ctx1 ctx2 bv1))] - (map #(vec [% (get-in bv2 [% :extent])]) (keys bv2)))) + (cover-to-concepts bv2))) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 0d34402aa..9bb817eb8 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -12,10 +12,8 @@ [conexp.fca.concept-transform :refer :all] [conexp.fca.cover :refer [generate-concept-cover]] [clojure.math.combinatorics :as comb] - [loom.graph :as lg] - [loom.alg :as la] - [clojure.core.reducers :as r]) - (:import [org.dimdraw Bipartite])) + [loom.graph :as lg] [loom.alg :as la] + [clojure.core.reducers :as r])) (defprotocol Smeasure (context [sm] "Returns the original context that is measured.") @@ -205,14 +203,16 @@ (rename-scale :attributes sm rename-fn)))) (defn- valid-cluster - "This function is a predicate factory for valid scale measure clustering." + "This function is a predicate factory for scale measure + clustering. Original is the cover structure of the original contexts + concepts." [scale original] - (let [get-exts (fn [cover] (set (map #(get-in cover [% :extent]) (keys cover)))) + (let [get-exts (fn [cover] (set (map #(get-in cover [% ::extent]) (keys cover)))) ext (get-exts original)] (fn [clustered-scale pre-image] (let [ext-new (get-exts (transform-bv-cover scale clustered-scale original))] - (subset? (set (map pre-image) ext-new) ext))))) + (subset? (set (map pre-image ext-new)) ext))))) (defmulti cluster-applier "Clusters attributes or objects in the scale context. @@ -225,7 +225,7 @@ (alter-meta! #'cluster-applier assoc :private true) -(defmethod cluster-applier [:attributes :ex] +(defmethod cluster-applier [:attributes ::ex] [_ _ ctx] (let [i (incidence-relation ctx)] (fn [attr] (make-context (objects ctx) @@ -236,7 +236,7 @@ b) ((incidence ctx) [a b]))))))) -(defmethod cluster-applier [:attributes :all] +(defmethod cluster-applier [:attributes ::all] [_ _ ctx] (let [i (incidence-relation ctx)] (fn [attr] @@ -249,7 +249,7 @@ b) ((incidence ctx) [a b]))))))) -(defmethod cluster-applier [:objects :all] +(defmethod cluster-applier [:objects ::all] [_ _ ctx] (fn [obj] (make-context (conj (difference (objects ctx) obj) obj) (attributes ctx) @@ -259,7 +259,7 @@ a) ((incidence ctx) [a b])))))) -(defmethod cluster-applier [:objects :ex] +(defmethod cluster-applier [:objects ::ex] [_ _ ctx] (fn [obj] (make-context (conj (difference (objects ctx) obj) obj) (attributes ctx) @@ -301,15 +301,16 @@ broken (some not-closed? pre-images); returns first non extent of lowest cardinality rev-broken (if broken (some not-closed? rev-pre-images) nil)] (if broken - (let [fixed-intent (if (= quant :all) + (let [fixed-intent (if (= quant ::all) (object-derivation broken-scale (reduce conj #{} (map image rev-broken))) (reduce into #{} (map (partial object-derivation broken-scale) (map (partial conj #{}) - (map image broken))))) ;; TODO need different derivation for :ex + (map image broken))))) ;; TODO need different derivation for ::ex fixed-extent (reduce conj #{} (map image broken)) [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 - (sort-by (comp count second) [[:objects fixed-extent] [:attributes fixed-intent]]))) + (sort-by (comp count second) [[:objects fixed-extent] + [:attributes fixed-intent]]))) apply-flattened-cluster (flattened-cluster-applier broken-scale kind quant)] (recur (apply-flattened-cluster fixed-cluster))) broken-scale)))) @@ -321,10 +322,10 @@ [sm init-cluster apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image] (loop [i 0] (let [candidates (build-candidates i) - valids (filter valid-cluster? - candidates)] + valids (filter valid-cluster? + candidates)] (if candidates - (if (empty? valids) + (if (empty? valids) (recur (inc i)) (if (empty? (first valids)) (let [new-scale (apply-cluster init-cluster)] @@ -336,6 +337,9 @@ (map #(into init-cluster %) valids))) nil)))) +(derive ::all ::quant) +(derive ::ex ::quant) + (defmulti cluster "Clusters attributes or objects in the scale context. For example the set #{1 2 3} become #{[1 2] 3} in the scale. The @@ -344,88 +348,141 @@ attribute/object clusters with existential and all quantified incidence." (fn [type quantifier & args] [type quantifier])) -(alter-meta! #'cluster assoc :private true) -(defmethod cluster [:attributes :all] - [_ _ sm attr] + +(defmethod cluster [:attributes ::all] + [_ _ sm attr & {:keys [flat]}] (let [ctx (context sm) - s (scale sm) - apply-cluster (cluster-applier :attributes :all s)] - (make-smeasure-nc (context sm) (apply-cluster attr) (measure sm)))) - -(defmethod cluster [:attributes :ex] - [_ _ sm attr & [smart]] - (let [s (scale sm)] - (if smart - (let [encode (fn [ctx] (-> ctx - (rename-attributes (fn [a] #{a})) - (rename-objects (fn [b] #{b})))) - decode (fn [ctx] (-> ctx - (rename-attributes (fn [a] (if (< 1 (count a)) a (first a)))) - (rename-objects (fn [b] (if (< 1 (count b)) b (first b)))))) - apply-flattened-cluster (flattened-cluster-applier :attributes :ex (encode s))] - (decode (repair-cluster :all (context sm) (apply-flattened-cluster attr)))) - (let [apply-cluster (cluster-applier :attributes :ex s) - original (generate-concept-cover (concepts s)) - comp-scale-image identity - scale-pre-image (constantly identity) - ;valid-cluster? (valid-cluster s original) - - valid-cluster? (fn [additional-attr] (if ((valid-cluster s original) - (apply-cluster (into attr additional-attr)) - (scale-pre-image (into attr additional-attr))) - additional-attr false)) - build-candidates (fn [i] (comb/combinations (seq (difference (attributes s) attr)) i))] - (cluster-until-valid - sm attr apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))))) + s (scale sm)] + (cond + flat (let [encoder (fn [a] (if (coll? a) (set a) #{a})) + decoder (fn [a] (if (< 1 (count a)) a (first a))) + ctx-encoder (fn [ctx] (-> ctx + (rename-attributes encoder) + (rename-objects encoder))) + ctx-decoder (fn [ctx] (-> ctx + (rename-attributes decoder) + (rename-objects decoder))) + apply-flattened-cluster (flattened-cluster-applier (ctx-encoder s) :attributes ::ex )] + (make-smeasure-nc ctx + (ctx-decoder (apply-flattened-cluster (map encoder attr))) + (measure sm))) + :else (let [apply-cluster (cluster-applier :attributes ::all s)] + (make-smeasure-nc (context sm) (apply-cluster attr) (measure sm)))))) + +(defmethod cluster [:attributes ::ex] + [_ _ sm attr & {:keys [flat no-check original]}] + (let [ctx (context sm) + s (scale sm)] + (cond + (and flat no-check) (let [encoder (fn [a] (if (coll? a) (set a) #{a})) + decoder (fn [a] (if (< 1 (count a)) a (first a))) + ctx-encoder (fn [ctx] (-> ctx + (rename-attributes encoder) + (rename-objects encoder))) + ctx-decoder (fn [ctx] (-> ctx + (rename-attributes decoder) + (rename-objects decoder))) + apply-flattened-cluster (flattened-cluster-applier (ctx-encoder s) :attributes ::ex)] + (make-smeasure-nc ctx + (ctx-decoder (apply-flattened-cluster (map encoder attr))) + (measure sm))) + flat (let [encoder (fn [a] (if (coll? a) (set a) #{a})) + decoder (fn [a] (if (< 1 (count a)) a (first a))) + ctx-encoder (fn [ctx] (-> ctx + (rename-attributes encoder) + (rename-objects encoder))) + ctx-decoder (fn [ctx] (-> ctx + (rename-attributes decoder) + (rename-objects decoder))) + + apply-flattened-cluster (flattened-cluster-applier (ctx-encoder s) :attributes ::ex ) + original (if original original (generate-concept-cover (concepts s))) + valid-cluster? (valid-cluster s original) + clustered (ctx-decoder (apply-flattened-cluster (map encoder attr)))] + (if (valid-cluster? clustered (measure sm)) + (make-smeasure-nc ctx clustered (measure sm)) + (do (println attr "is not a valid clustering") sm))) + no-check (let [apply-cluster (cluster-applier :attributes ::ex s)] + (make-smeasure-nc (context sm) (apply-cluster attr) (measure sm))) + :else (let [apply-cluster (cluster-applier :attributes ::ex s) + original (if original original (generate-concept-cover (concepts s))) + valid-cluster? (valid-cluster s original) + clustered (apply-cluster attr) + ;; comp-scale-image identity + ;; scale-pre-image (constantly identity) + + ;; valid-cluster? (fn [additional-attr] (if ((valid-cluster s original) + ;; (apply-cluster (into attr additional-attr)) + ;; (scale-pre-image (into attr additional-attr))) + ;; additional-attr false)) + ;; build-candidates (fn [i] (comb/combinations (seq (difference (attributes s) attr)) i))] + ;; (cluster-until-valid + ;; sm attr apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image) + ] + (if (valid-cluster? clustered (measure sm)) + (make-smeasure-nc ctx clustered (measure sm)) + (do (println attr "is not a valid clustering") sm)))))) -(defmethod cluster [:objects :all] - [_ _ sm obj & [smart]] - (let [s (scale sm)] - (if smart - (let [encode (fn [ctx] (-> ctx - (rename-attributes (fn [a] #{a})) - (rename-objects (fn [b] #{b})))) - decode (fn [ctx] (-> ctx - (rename-attributes (fn [a] (if (< 1 (count a)) a (first a)))) - (rename-objects (fn [b] (if (< 1 (count b)) b (first b)))))) - apply-flattened-cluster (flattened-cluster-applier :objects :all (encode s))] - (decode (repair-cluster :all (context sm) (apply-flattened-cluster obj)))) - (let [apply-cluster (cluster-applier :objects :all s) - original (generate-concept-cover (concepts s)) - comp-scale-image (fn [g] (if (contains? obj g) obj g)) - scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) - valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) - (apply-cluster (into obj additional-obj)) - (scale-pre-image (into obj additional-obj))) - additional-obj false)) - build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] - (cluster-until-valid - sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))))) - -(defmethod cluster [:objects :ex] - [_ _ sm obj & [smart]] - (let [s (scale sm)] - (if smart - (let [encode (fn [ctx] (-> ctx - (rename-attributes (fn [a] #{a})) - (rename-objects (fn [b] #{b})))) - decode (fn [ctx] (-> ctx - (rename-attributes (fn [a] (if (< 1 (count a)) a (first a)))) - (rename-objects (fn [b] (if (< 1 (count b)) b (first b)))))) - apply-flattened-cluster (flattened-cluster-applier :objects :ex (encode s))] - (decode (repair-cluster :all (context sm) (apply-flattened-cluster obj)))) - (let [apply-cluster (cluster-applier :objects :ex s) - original (generate-concept-cover (concepts s)) - comp-scale-image (fn [g] (if (contains? obj g) obj g)) - scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) - valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) - (apply-cluster (into obj additional-obj)) - (scale-pre-image (into obj additional-obj))) - additional-obj false)) - build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] - (cluster-until-valid - sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image))))) +;;repair new map for flattened cluster +(defmethod cluster [:objects ::quant] + [_ quant sm obj & {:keys [flat no-check original]}] + (let [ctx (context sm) + s (scale sm)] + (cond + (and flat no-check) (let [encoder (fn [a] (if (coll? a) (set a) #{a})) + decoder (fn [a] (if (< 1 (count a)) a (first a))) + ctx-encoder (fn [ctx] (-> ctx + (rename-attributes encoder) + (rename-objects encoder))) + ctx-decoder (fn [ctx] (-> ctx + (rename-attributes decoder) + (rename-objects decoder))) + apply-flattened-cluster (flattened-cluster-applier (ctx-encoder s) :objects quant) + clustered (ctx-decoder (apply-flattened-cluster (set (map encoder obj)))) + new-map (fn [o] + (let [entailed (some #(if (contains? % o) % nil) (filter coll? (objects clustered)))] + (if entailed entailed o)))] + (make-smeasure-nc ctx clustered new-map)) + flat (let [encoder (fn [a] (if (coll? a) (set a) #{a})) + decoder (fn [a] (if (< 1 (count a)) a (first a))) + ctx-encoder (fn [ctx] (-> ctx + (rename-attributes encoder) + (rename-objects encoder))) + ctx-decoder (fn [ctx] (-> ctx + (rename-attributes decoder) + (rename-objects decoder))) + apply-flattened-cluster (flattened-cluster-applier (ctx-encoder s) :objects quant ) + original (if original original (generate-concept-cover (concepts s))) + valid-cluster? (valid-cluster s original) + clustered (ctx-decoder (apply-flattened-cluster obj)) + new-map (fn [o] (if (contains? obj ((measure sm) o)) (set (flatten obj)) ((measure sm) o)))] + (if (valid-cluster? clustered (measure sm)) + (make-smeasure-nc ctx clustered new-map) + (do (println obj "is not a valid clustering") sm))) + no-check (let [apply-cluster (cluster-applier :objects quant s) + clustered (apply-cluster obj) + new-map (fn [o] (if (contains? obj ((measure sm) o)) obj ((measure sm) o)))] + (make-smeasure-nc ctx clustered new-map) ) + :else (let [apply-cluster (cluster-applier :objects quant s) + original (if original original (generate-concept-cover (concepts s))) + valid-cluster? (valid-cluster s original) + clustered (apply-cluster obj) + new-map (fn [o] (if (contains? obj ((measure sm) o)) obj ((measure sm) o))) + ;; comp-scale-image (fn [g] (if (contains? obj g) obj g)) + ;; scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) + + ;; valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) + ;; (apply-cluster (into obj additional-obj)) + ;; (scale-pre-image (into obj additional-obj))) + ;; additional-obj false)) + ;; build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] + ;; (cluster-until-valid + ;; sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image) + ] + (if (valid-cluster? clustered (measure sm)) + (make-smeasure-nc ctx clustered new-map) + (do (println obj "is not a valid clustering") sm)))))) (defn- flattened-cluster "This is a wrapper method to flatten the cluster result." @@ -440,6 +497,47 @@ #{} k)))) nil))) +;;; tester for valid cluster sets +(defmulti valid-cluster-set + "This method checks, if a set of objects/attributes can be clustered + in a context to yield a valid scale measure." + (fn [type quantifier & args] [type quantifier])) + +(defmethod valid-cluster-set [:attributes ::all] + [_ quant ctx attr] + true) + +(defmethod valid-cluster-set [:attributes ::ex] + [_ quant ctx attr] + (let [cluster-deri (apply union (map #(attribute-derivation ctx #{%}) attr))] + (extent? ctx cluster-deri))) + +(defmethod valid-cluster-set [:objects ::all] + [_ quant ctx obj] + (let [exts (extents ctx)] + (not (some #(not (contains? exts (difference % obj))) exts)))) + +(defmethod valid-cluster-set [:objects ::ex] + [_ quant ctx obj] + (let [cluster-deri (apply union (map #(object-derivation ctx #{%}) obj)) + con (concepts ctx)] + (not (some #(and (subset? (second %) cluster-deri) + (not (extent? (union (first %) obj)))) con)))) + +(defn all-cluster-candidates +"This methods computes all sets of attributes/objects that yield a + scale measure. The computed sets can be limited to a size or to be + supersets of an input." + [kind quant ctx {:keys [size init-set]}] + (let [get-set (kind {:attributes attributes :objects objects}) + init (if init-set init-set #{}) + limit (- (if size size (count (get-set ctx))) (count init))] + (filter (partial kind quant ctx) + (map #(union % init) + (apply concat + (for [n (range (inc limit))] + (comb/combinations (get-set ctx) n))))))) + (defn- incompatibility-graph "For a formal context computes the imcompatibility graph of its incidence relation." @@ -538,7 +636,7 @@ (let [default-args {:generation-size 10 :generations 10 :survival-ratio 0.3 :mutation-rate 0.3 :fresh-chance 0.05 :mode :incidence-clustered - :quant :all + :quant ::all :init {:objects #{} :attributes #{}} :init-cluster (fn [ctx] {:objects (reduce #(conj %1 #{%2}) #{} (objects ctx)) @@ -646,8 +744,8 @@ "This Method is a genetic algorithm to determine a scale whichs concept lattice is of order dimension 2D. The methods simulated by this algorithm are cluster methods only and for comprehensibility we - use only one cluster variation (:all, :or) at a time. Further note - that nested clusters of the same type (:all, :ex) are equivalent to + use only one cluster variation (::all, :or) at a time. Further note + that nested clusters of the same type (::all, ::ex) are equivalent to their flattened correspondence. This method uses a genetic algorithm that determines a large sub-context, i.e. the number of objects times attributes, whichs concept lattice is of order dimension at @@ -663,7 +761,7 @@ to-sm (fn [scale] (make-smeasure-nc ctx scale (fn [g] (if (contains? (objects scale) g) g (some (fn [o] (and (set? o) (contains? o g))) - (objects c))))))] + (objects scale))))))] (loop [n (:generations args) generation (first-generation args ctx init-ind graph)] (println "Generation: " (- (:generations args) n)) @@ -778,10 +876,10 @@ #(read-string (str (read-line))) #(or (= :objects %) (= :attributes %)) "The input must be :attributes or :objects: \n") - cluster-incidence (ask (str "Please enter if their common (:all) or conjoined (:ex) incidence is used as new cluster incidences: \n") + cluster-incidence (ask (str "Please enter if their common (::all) or conjoined (::ex) incidence is used as new cluster incidences: \n") #(read-string (str (read-line))) - #(or (= :all %) (= :ex %)) - "The input must be :all or :ex: \n") + #(or (= ::all %) (= ::ex %)) + "The input must be ::all or ::ex: \n") cluster-method (partial cluster cluster-kind cluster-incidence) cluster-content (ask (str "Please enter all " (cluster-kind {:attributes "attributes" :objects "objects"}) " to be clustered with ; seperator: \n") #(set (map read-string (clojure.string/split (str (read-line)) #";"))) diff --git a/src/main/clojure/conexp/io/smeasure.clj b/src/main/clojure/conexp/io/smeasure.clj index f6f213fc5..5c65a8863 100644 --- a/src/main/clojure/conexp/io/smeasure.clj +++ b/src/main/clojure/conexp/io/smeasure.clj @@ -285,7 +285,7 @@ anchor (last (butlast (attributes ctx)))] (doall (if (>= 2 (count (str anchor))) (do - (println (str " \\node[right = 0.45cm of ca" +v (println (str " \\node[right = 0.45cm of ca" (tex-escape anchor) "] (za) {};")) (println (str " \\node[below = 0.25cm of za] (co" From e318951ea5dccad5252eb12794c383c665abf87c Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Mon, 26 Oct 2020 11:41:13 +0100 Subject: [PATCH 037/117] Scale-Measure init restructure --- src/main/clojure/conexp/fca/smeasure.clj | 38 +++++++++++++----------- 1 file changed, 21 insertions(+), 17 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 9bb817eb8..3b97b0392 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -508,36 +508,40 @@ true) (defmethod valid-cluster-set [:attributes ::ex] - [_ quant ctx attr] - (let [cluster-deri (apply union (map #(attribute-derivation ctx #{%}) attr))] + [_ quant ctx attr & {:keys [old-ctx]}] + (let [ctx (if old-ctx old-ctx ctx) + cluster-deri (apply union (map #(attribute-derivation ctx #{%}) attr))] (extent? ctx cluster-deri))) (defmethod valid-cluster-set [:objects ::all] - [_ quant ctx obj] - (let [exts (extents ctx)] + [_ quant ctx obj & {:keys [exts]}] + (let [exts (if exts exts (set (extents ctx)))] (not (some #(not (contains? exts (difference % obj))) exts)))) (defmethod valid-cluster-set [:objects ::ex] - [_ quant ctx obj] + [_ quant ctx obj & {:keys [exts]}] (let [cluster-deri (apply union (map #(object-derivation ctx #{%}) obj)) - con (concepts ctx)] - (not (some #(and (subset? (second %) cluster-deri) - (not (extent? (union (first %) obj)))) con)))) + exts (if exts exts (extents ctx))] + (not (some #(and (subset? (object-derivation ctx (difference % obj)) cluster-deri) + (not (extent? ctx (union % obj)))) exts)))) (defn all-cluster-candidates "This methods computes all sets of attributes/objects that yield a scale measure. The computed sets can be limited to a size or to be supersets of an input." - [kind quant ctx {:keys [size init-set]}] - (let [get-set (kind {:attributes attributes :objects objects}) + [kind quant ctx & {:keys [size init-set]}] + (let [get-set (get {:attributes attributes :objects objects} kind) init (if init-set init-set #{}) - limit (- (if size size (count (get-set ctx))) (count init))] - (filter (partial kind quant ctx) - (map #(union % init) - (apply concat - (for [n (range (inc limit))] - (comb/combinations (get-set ctx) n))))))) - + limit (- (if size size (count (get-set ctx))) (count init)) + base (vec (get-set ctx))] + + (r/foldcat + (r/filter #(valid-cluster-set kind quant ctx (into #{} %)) + (r/map #(union % init) + (r/fold concat + (map #(comb/combinations base %) + (range (inc limit))))))))) + (defn- incompatibility-graph "For a formal context computes the imcompatibility graph of its incidence relation." From 88b471f511864bb3d632c0e4a8e8ffaef922f5c3 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Mon, 26 Oct 2020 14:06:57 +0100 Subject: [PATCH 038/117] Scale-Measures Added logical attributes --- src/main/clojure/conexp/fca/smeasure.clj | 688 ++--------------------- 1 file changed, 60 insertions(+), 628 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 3b97b0392..c7e662e92 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -202,582 +202,10 @@ rename-fn (fn [a] (or (get rename-map a) a))] (rename-scale :attributes sm rename-fn)))) -(defn- valid-cluster - "This function is a predicate factory for scale measure - clustering. Original is the cover structure of the original contexts - concepts." - [scale original] - (let [get-exts (fn [cover] (set (map #(get-in cover [% ::extent]) (keys cover)))) - ext (get-exts original)] - (fn [clustered-scale pre-image] - (let [ext-new (get-exts (transform-bv-cover scale clustered-scale original))] - - (subset? (set (map pre-image ext-new)) ext))))) - -(defmulti cluster-applier - "Clusters attributes or objects in the scale context. - For exaegawegaewrgaewrgsfagfagewgwegwegwegmple the set #{1 2 3} become #{[1 2] 3} in the scale. The - new incidence is build such that (g, [1 2]) if (g,m) for all/some m - in [1 2] in the case of attributes. Possible clusters are - attribute/object clusters with existential and all quantified - incidence." - (fn [type quantifier & args] [type quantifier])) -(alter-meta! #'cluster-applier assoc :private true) - - -(defmethod cluster-applier [:attributes ::ex] - [_ _ ctx] - (let [i (incidence-relation ctx)] - (fn [attr] (make-context (objects ctx) - (conj (difference (attributes ctx) attr) attr) - (fn [a b] - (if (= attr b) - (some #((incidence ctx) [a %]) - b) - ((incidence ctx) [a b]))))))) - -(defmethod cluster-applier [:attributes ::all] - [_ _ ctx] - (let [i (incidence-relation ctx)] - (fn [attr] - (make-context (objects ctx) - (conj (difference (set (attributes ctx)) attr) - attr) - (fn [a b] - (if (= attr b) - (every? #((incidence ctx) [a %]) - b) - ((incidence ctx) [a b]))))))) - -(defmethod cluster-applier [:objects ::all] - [_ _ ctx] - (fn [obj] (make-context (conj (difference (objects ctx) obj) obj) - (attributes ctx) - (fn [a b] - (if (= a obj) - (every? #((incidence ctx) [% b]) - a) - ((incidence ctx) [a b])))))) - -(defmethod cluster-applier [:objects ::ex] - [_ _ ctx] - (fn [obj] (make-context (conj (difference (objects ctx) obj) obj) - (attributes ctx) - (fn [a b] - (if (= obj a) - (some #((incidence ctx) [% b]) - a) - ((incidence ctx) [a b])))))) - -(defn- flattened-cluster-applier - "Returns a cluster method depending on the 'kind and 'quant specifier." - [ctx kind quant] - (fn [cl] (-> ((cluster-applier kind quant ctx) cl) - (rename-objects (fn [o] - (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) - #{} o))) - (rename-attributes (fn [a] - (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) - #{} a)))))) - -; todo check if smast cluster works after ordinary cluster - -(defn- repair-cluster - "Given a scale context constructs a valid smeasure scale by using as - few cluster methods as possible. 'quantifier specifies the cluster - quantifier used by the clustering methods." - [quant ctx s] - (loop [broken-scale s] - (let [br-exts (extents broken-scale) - ;todo smallest ext and repair obj or largest and repair attr - pre-images (sort-by count - (map (partial reduce into #{}) ;; pre-image: no renamed used and clusters are flat - br-exts)) - rev-pre-images (reverse pre-images) - not-closed? (fn [e] (let [orig-e (context-object-closure ctx e)] - (if (= orig-e e) nil orig-e))) - image (fn [o] (some - #(if (contains? % o) % false) (objects broken-scale))) - broken (some not-closed? pre-images); returns first non extent of lowest cardinality - rev-broken (if broken (some not-closed? rev-pre-images) nil)] - (if broken - (let [fixed-intent (if (= quant ::all) - (object-derivation broken-scale (reduce conj #{} (map image rev-broken))) - (reduce into #{} - (map (partial object-derivation broken-scale) - (map (partial conj #{}) - (map image broken))))) ;; TODO need different derivation for ::ex - fixed-extent (reduce conj #{} (map image broken)) - [kind fixed-cluster] (first (filter #(-> % second count (> 1)) ;get smallest greater 1 - (sort-by (comp count second) [[:objects fixed-extent] - [:attributes fixed-intent]]))) - apply-flattened-cluster (flattened-cluster-applier broken-scale kind quant)] - (recur (apply-flattened-cluster fixed-cluster))) - broken-scale)))) - -(defn- cluster-until-valid - "This is a helper method, that applies a certain clustering until a - valid scale measure is outputted. If not unique, returns a seq of - valid candidates." - [sm init-cluster apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image] - (loop [i 0] - (let [candidates (build-candidates i) - valids (filter valid-cluster? - candidates)] - (if candidates - (if (empty? valids) - (recur (inc i)) - (if (empty? (first valids)) - (let [new-scale (apply-cluster init-cluster)] - (make-smeasure-nc (context sm) - (make-context (objects new-scale) - (attributes new-scale) - (incidence-relation new-scale)) - (comp comp-scale-image (measure sm)))) - (map #(into init-cluster %) valids))) - nil)))) (derive ::all ::quant) (derive ::ex ::quant) -(defmulti cluster - "Clusters attributes or objects in the scale context. - For example the set #{1 2 3} become #{[1 2] 3} in the scale. The - new incidence is build such that (g, [1 2]) if (g,m) for all/some m - in [1 2] in the case of attributes. Possible clusters are - attribute/object clusters with existential and all quantified - incidence." - (fn [type quantifier & args] [type quantifier])) - - -(defmethod cluster [:attributes ::all] - [_ _ sm attr & {:keys [flat]}] - (let [ctx (context sm) - s (scale sm)] - (cond - flat (let [encoder (fn [a] (if (coll? a) (set a) #{a})) - decoder (fn [a] (if (< 1 (count a)) a (first a))) - ctx-encoder (fn [ctx] (-> ctx - (rename-attributes encoder) - (rename-objects encoder))) - ctx-decoder (fn [ctx] (-> ctx - (rename-attributes decoder) - (rename-objects decoder))) - apply-flattened-cluster (flattened-cluster-applier (ctx-encoder s) :attributes ::ex )] - (make-smeasure-nc ctx - (ctx-decoder (apply-flattened-cluster (map encoder attr))) - (measure sm))) - :else (let [apply-cluster (cluster-applier :attributes ::all s)] - (make-smeasure-nc (context sm) (apply-cluster attr) (measure sm)))))) - -(defmethod cluster [:attributes ::ex] - [_ _ sm attr & {:keys [flat no-check original]}] - (let [ctx (context sm) - s (scale sm)] - (cond - (and flat no-check) (let [encoder (fn [a] (if (coll? a) (set a) #{a})) - decoder (fn [a] (if (< 1 (count a)) a (first a))) - ctx-encoder (fn [ctx] (-> ctx - (rename-attributes encoder) - (rename-objects encoder))) - ctx-decoder (fn [ctx] (-> ctx - (rename-attributes decoder) - (rename-objects decoder))) - apply-flattened-cluster (flattened-cluster-applier (ctx-encoder s) :attributes ::ex)] - (make-smeasure-nc ctx - (ctx-decoder (apply-flattened-cluster (map encoder attr))) - (measure sm))) - flat (let [encoder (fn [a] (if (coll? a) (set a) #{a})) - decoder (fn [a] (if (< 1 (count a)) a (first a))) - ctx-encoder (fn [ctx] (-> ctx - (rename-attributes encoder) - (rename-objects encoder))) - ctx-decoder (fn [ctx] (-> ctx - (rename-attributes decoder) - (rename-objects decoder))) - - apply-flattened-cluster (flattened-cluster-applier (ctx-encoder s) :attributes ::ex ) - original (if original original (generate-concept-cover (concepts s))) - valid-cluster? (valid-cluster s original) - clustered (ctx-decoder (apply-flattened-cluster (map encoder attr)))] - (if (valid-cluster? clustered (measure sm)) - (make-smeasure-nc ctx clustered (measure sm)) - (do (println attr "is not a valid clustering") sm))) - no-check (let [apply-cluster (cluster-applier :attributes ::ex s)] - (make-smeasure-nc (context sm) (apply-cluster attr) (measure sm))) - :else (let [apply-cluster (cluster-applier :attributes ::ex s) - original (if original original (generate-concept-cover (concepts s))) - valid-cluster? (valid-cluster s original) - clustered (apply-cluster attr) - ;; comp-scale-image identity - ;; scale-pre-image (constantly identity) - - ;; valid-cluster? (fn [additional-attr] (if ((valid-cluster s original) - ;; (apply-cluster (into attr additional-attr)) - ;; (scale-pre-image (into attr additional-attr))) - ;; additional-attr false)) - ;; build-candidates (fn [i] (comb/combinations (seq (difference (attributes s) attr)) i))] - ;; (cluster-until-valid - ;; sm attr apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image) - ] - (if (valid-cluster? clustered (measure sm)) - (make-smeasure-nc ctx clustered (measure sm)) - (do (println attr "is not a valid clustering") sm)))))) - -;;repair new map for flattened cluster -(defmethod cluster [:objects ::quant] - [_ quant sm obj & {:keys [flat no-check original]}] - (let [ctx (context sm) - s (scale sm)] - (cond - (and flat no-check) (let [encoder (fn [a] (if (coll? a) (set a) #{a})) - decoder (fn [a] (if (< 1 (count a)) a (first a))) - ctx-encoder (fn [ctx] (-> ctx - (rename-attributes encoder) - (rename-objects encoder))) - ctx-decoder (fn [ctx] (-> ctx - (rename-attributes decoder) - (rename-objects decoder))) - apply-flattened-cluster (flattened-cluster-applier (ctx-encoder s) :objects quant) - clustered (ctx-decoder (apply-flattened-cluster (set (map encoder obj)))) - new-map (fn [o] - (let [entailed (some #(if (contains? % o) % nil) (filter coll? (objects clustered)))] - (if entailed entailed o)))] - (make-smeasure-nc ctx clustered new-map)) - flat (let [encoder (fn [a] (if (coll? a) (set a) #{a})) - decoder (fn [a] (if (< 1 (count a)) a (first a))) - ctx-encoder (fn [ctx] (-> ctx - (rename-attributes encoder) - (rename-objects encoder))) - ctx-decoder (fn [ctx] (-> ctx - (rename-attributes decoder) - (rename-objects decoder))) - apply-flattened-cluster (flattened-cluster-applier (ctx-encoder s) :objects quant ) - original (if original original (generate-concept-cover (concepts s))) - valid-cluster? (valid-cluster s original) - clustered (ctx-decoder (apply-flattened-cluster obj)) - new-map (fn [o] (if (contains? obj ((measure sm) o)) (set (flatten obj)) ((measure sm) o)))] - (if (valid-cluster? clustered (measure sm)) - (make-smeasure-nc ctx clustered new-map) - (do (println obj "is not a valid clustering") sm))) - no-check (let [apply-cluster (cluster-applier :objects quant s) - clustered (apply-cluster obj) - new-map (fn [o] (if (contains? obj ((measure sm) o)) obj ((measure sm) o)))] - (make-smeasure-nc ctx clustered new-map) ) - :else (let [apply-cluster (cluster-applier :objects quant s) - original (if original original (generate-concept-cover (concepts s))) - valid-cluster? (valid-cluster s original) - clustered (apply-cluster obj) - new-map (fn [o] (if (contains? obj ((measure sm) o)) obj ((measure sm) o))) - ;; comp-scale-image (fn [g] (if (contains? obj g) obj g)) - ;; scale-pre-image (fn [o] (fn [oset] (reduce #(if (= o %2) (into %1 %2) (conj %1 %2)) #{} oset))) - - ;; valid-cluster? (fn [additional-obj] (if ((valid-cluster s original) - ;; (apply-cluster (into obj additional-obj)) - ;; (scale-pre-image (into obj additional-obj))) - ;; additional-obj false)) - ;; build-candidates (fn [i] (comb/combinations (seq (difference (objects s) obj)) i))] - ;; (cluster-until-valid - ;; sm obj apply-cluster valid-cluster? build-candidates comp-scale-image scale-pre-image) - ] - (if (valid-cluster? clustered (measure sm)) - (make-smeasure-nc ctx clustered new-map) - (do (println obj "is not a valid clustering") sm)))))) - -(defn- flattened-cluster - "This is a wrapper method to flatten the cluster result." - [kind quant sm thing] - (let [result (cluster kind quant sm thing)] - (if result - (if (coll? result) - (map (partial reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) #{}) - result) - (rename-scale kind result (fn [k] - (reduce #(if (coll? %2) (into %1 %2) (conj %1 %2)) - #{} k)))) - nil))) - -;;; tester for valid cluster sets -(defmulti valid-cluster-set - "This method checks, if a set of objects/attributes can be clustered - in a context to yield a valid scale measure." - (fn [type quantifier & args] [type quantifier])) - -(defmethod valid-cluster-set [:attributes ::all] - [_ quant ctx attr] - true) - -(defmethod valid-cluster-set [:attributes ::ex] - [_ quant ctx attr & {:keys [old-ctx]}] - (let [ctx (if old-ctx old-ctx ctx) - cluster-deri (apply union (map #(attribute-derivation ctx #{%}) attr))] - (extent? ctx cluster-deri))) - -(defmethod valid-cluster-set [:objects ::all] - [_ quant ctx obj & {:keys [exts]}] - (let [exts (if exts exts (set (extents ctx)))] - (not (some #(not (contains? exts (difference % obj))) exts)))) - -(defmethod valid-cluster-set [:objects ::ex] - [_ quant ctx obj & {:keys [exts]}] - (let [cluster-deri (apply union (map #(object-derivation ctx #{%}) obj)) - exts (if exts exts (extents ctx))] - (not (some #(and (subset? (object-derivation ctx (difference % obj)) cluster-deri) - (not (extent? ctx (union % obj)))) exts)))) - -(defn all-cluster-candidates -"This methods computes all sets of attributes/objects that yield a - scale measure. The computed sets can be limited to a size or to be - supersets of an input." - [kind quant ctx & {:keys [size init-set]}] - (let [get-set (get {:attributes attributes :objects objects} kind) - init (if init-set init-set #{}) - limit (- (if size size (count (get-set ctx))) (count init)) - base (vec (get-set ctx))] - - (r/foldcat - (r/filter #(valid-cluster-set kind quant ctx (into #{} %)) - (r/map #(union % init) - (r/fold concat - (map #(comb/combinations base %) - (range (inc limit))))))))) - -(defn- incompatibility-graph - "For a formal context computes the imcompatibility graph of its - incidence relation." - [ctx] - (let [nodes (difference (cross-product (objects ctx) (attributes ctx)) - (incidence-relation ctx)) - incompatible? (fn [[[g m] [h n]]] - (and ((incidence ctx) [g n]) - ((incidence ctx) [h m]))) - edges (r/foldcat (r/filter incompatible? (cross-product nodes nodes)))] - (apply lg/graph edges))) - -(defn- updated-incompatibility-graph - [graph scale] - (let [new-nodes (difference (cross-product (objects scale) (attributes scale)) - (incidence-relation scale)) - sub (lg/subgraph graph (intersection (lg/nodes graph) new-nodes)) - - incompatible? (fn [[[g m] [h n]]] - (and ((incidence scale) [g n]) - ((incidence scale) [h m]))) - new-edges (filter incompatible? (cross-product (difference new-nodes (lg/nodes graph)) new-nodes))] - (apply lg/add-edges sub new-edges))) - -(defn- cluster-ind-intersecter - "This method computed the intersection between two cluster individuals by computing the splittance." - [{iobjs1 :objects iattr1 :attributes :as ind1} - {iobjs2 :objects iattr2 :attributes :as ind2}] - {:objects (->> iobjs2 - ;; computes splitance - (reduce (fn [tmp-ind cl] (union (set (map #(difference % cl) tmp-ind)) - (set (map #(intersection % cl) tmp-ind)))) - iobjs1) - ;; remove empty fragment - (#(disj % #{}))) - :attributes (->> iattr2 - ;; computes splitance - (reduce (fn [tmp-ind cl] (union (set (map #(difference % cl) tmp-ind)) - (set (map #(intersection % cl) tmp-ind)))) - iattr1) - ;; remove empty fragment - (#(disj % #{})))}) - -;; first gen needs to convert each attribute/objects into a set -(defn- ind2clustered-ctx - "This is a helper method to apply the by the individual specified clustering." - [args ctx {iobjs :objects iattr :attributes :as ind}] - (let [apply-cluster-obj (fn [tocluster-ctx cl] ((cluster-applier :objects (:quant args) tocluster-ctx) cl)) - apply-cluster-attr (fn [tocluster-ctx cl] ((cluster-applier :attributes (:quant args) tocluster-ctx) cl))] - (reduce apply-cluster-obj (reduce apply-cluster-attr ctx iattr) - iobjs))) - -(defn- apply-small-rand-cluster - "This is a helper method to apply the smallest clustering out of a few - random valid clusterings." - [args ctx scale-ctx] - (let [kind (rand-nth [:attributes :objects]) - quant (:quant args) - candidates (if (and (= :objects kind) (-> scale-ctx objects count (= 1) not)) - (take 10 (partition 2 (shuffle (objects scale-ctx)))) - (take 10 (partition 2 (shuffle (attributes scale-ctx))))) - apply-flattened-cluster (flattened-cluster-applier scale-ctx kind quant) - - derivation-op (if (= kind :objects) object-derivation attribute-derivation) - key-fkt (fn [[a b]] (let [da (derivation-op scale-ctx #{a}) - db (derivation-op scale-ctx #{b})] - (+ (count (difference da db)) - (count (difference db da))))) - most-in-common (apply min-key key-fkt candidates) - smallest (repair-cluster quant ctx (apply-flattened-cluster (set most-in-common)))] - (if smallest smallest - (make-context #{(set (objects ctx))} #{(set (attributes ctx))} - #{[#{(set (objects ctx))} #{(set (attributes ctx))}]})))) ;TODO fix incidence - -(defn- fill-individual - "Inserts as many objects/attributes to the individual as possible. - An individual is a set of nodes of the contexts incompatibility graph." - [args ctx graph {iobjs :objects iattr :attributes :as ind}] - (let [repaired-ind (->> ind - (ind2clustered-ctx args ctx) - (repair-cluster (:quant args) ctx)) - make-ind-map #(hash-map :objects (objects %) :attributes (attributes %)) - new-graph (updated-incompatibility-graph graph repaired-ind)] - (loop [tmp-ind repaired-ind g new-graph] ;; apply small clusters until 2D - (if (la/bipartite? g) - (make-ind-map tmp-ind) - (let [new-ind (apply-small-rand-cluster args ctx tmp-ind) - new-g (updated-incompatibility-graph g new-ind)] - (recur new-ind new-g)))))) - -;;genetic algorithm - -(defn- make-args-map - "Returns default args updated by user input." - [args] - (let [default-args {:generation-size 10 :generations 10 - :survival-ratio 0.3 :mutation-rate 0.3 - :fresh-chance 0.05 :mode :incidence-clustered - :quant ::all - :init {:objects #{} :attributes #{}} - :init-cluster (fn [ctx] - {:objects (reduce #(conj %1 #{%2}) #{} (objects ctx)) - :attributes (reduce #(conj %1 #{%2}) #{} (attributes ctx))})}] - (assert (or (not (:init args)) - (la/bipartite? (incompatibility-graph (:init args)))) - "Inputted initial Context must have a concept lattice of - order dimension two.") - (let [combined-args - (-> (reduce #(assoc %1 %2 (%2 args)) default-args (keys args)) - (update :init #(if (context? %) - {:objects (objects %) :attributes (attributes %)} - %)))] - (assoc combined-args :survival-count (int (* (:generation-size combined-args) - (:survival-ratio combined-args))))))) - -(defmulti fitness - "For a bipartite incompatibility graph of a subset of attributes - and objects of a context, computes if adding an object/attribute - preserves the bipartite property." - (fn [args & params] (:mode args))) -(alter-meta! #'fitness assoc :private true) - -(defmethod fitness :concepts - [args ctx {iobjs :objects iattr :attributes :as ind}] - (-> (ind2clustered-ctx args ctx ind) - concepts - count)) - -(defmethod fitness :nontrivia - [args ctx {iobjs :objects iattr :attributes :as ind}] - (let [sub-ctx (ind2clustered-ctx args ctx ind) - nontrivia-obj (filter #(not (empty? (object-derivation sub-ctx #{%}))) - (objects sub-ctx)) - nontrivia-attr (filter #(not (empty? (attribute-derivation sub-ctx #{%}))) - (attributes sub-ctx))] - (* (count nontrivia-obj) - (count nontrivia-attr)))) - -(defmethod fitness :incidence - [args ctx {iobjs :objects iattr :attributes :as ind}] - (let [sub-ctx (ind2clustered-ctx args ctx ind)] - (count (incidence-relation sub-ctx)))) - -(defmethod fitness :default - [_ ctx {iobjs :objects iattr :attributes :as ind}] - (* (count iobjs) - (count iattr))) - -(defn- mutation - "Mutates the current individual by removing an object or attribute - given a probability." - [args ctx graph {iobjs :objects iattr :attributes :as ind}] - ;; (if (> (:fresh-chance args) (rand)) - ;; (fill-individual-cluster args ctx graph ((:init-cluster args) ctx))) - (let [mutated-obj (into #{} (random-sample (:mutation-rate args) iobjs)) - mutated-attr (into #{} (random-sample (:mutation-rate args) iattr))] - (-> ind - (assoc :objects (reduce (fn [ind-objs tomutate-obj-cl] ;; flattens the to mutate cluster #{1 2 3} -> #{1} #{2} #{3} - (reduce #(conj %1 #{%2}) ind-objs tomutate-obj-cl)) - (difference (:objects ind) mutated-obj) mutated-obj)) - (assoc :attributes (reduce (fn [ind-attr tomutate-attr-cl] - (reduce #(conj %1 #{%2}) ind-attr tomutate-attr-cl)) - (difference (:attributes ind) mutated-attr) mutated-attr))))) - -(defn- breeding - "Given two individuals, i.e. contexts, breeds a next new individual by - first computing the context of common attributes and - objects. Secondly as many attributes/objects of ctx are inserted - without increasing the order dimension of the new individual." - [args ctx graph ind1 ind2] - (->> (cluster-ind-intersecter ind1 ind2) - (mutation args ctx graph) - (fill-individual args ctx graph))) - -(defn- next-generation - "Given the current generation of contexts, breeds the next generation." - [args ctx graph generation] - (let [survivals (->> generation - (sort-by (partial fitness args ctx) >) ;; todo parallel fitness apply - (take (:survival-count args))) - pairing (->> survivals - shuffle - (partition 2)) - rand-pair (fn [] (->> survivals - shuffle - (take 2)))] - (into [] - (concat survivals - (->> (concat pairing (repeat (rand-pair))) - (take (- (:generation-size args) (:survival-count args))) - (into []) - (pmap (fn [[ind1 ind2]] (breeding args ctx graph ind1 ind2)))))))) - -(defn- first-generation - "Computes a first random generation of contexts with order dimension - at most two." - [args ctx init-ctx graph] - (into [] - (pmap (fn [i] - (fill-individual args ctx graph init-ctx)) - (range (:generation-size args))))) - -(defn- genetic-2d - "This Method is a genetic algorithm to determine a scale whichs - concept lattice is of order dimension 2D. The methods simulated by - this algorithm are cluster methods only and for comprehensibility we - use only one cluster variation (::all, :or) at a time. Further note - that nested clusters of the same type (::all, ::ex) are equivalent to - their flattened correspondence. This method uses a genetic algorithm - that determines a large sub-context, i.e. the number of objects - times attributes, whichs concept lattice is of order dimension at - most two. After that missing attributes are combined with existing - objects, attributes such that they preserve the order dimension." - [ctx & [args]] - (let [args (make-args-map (if (nil? args) {} args)) - init-ind ((:init-cluster args) ctx) - graph (incompatibility-graph (ind2clustered-ctx args ctx init-ind)) - decode (fn [ctx] (-> ctx - (rename-attributes (fn [a] (if (< 1 (count a)) a (first a)))) - (rename-objects (fn [b] (if (< 1 (count b)) b (first b)))))) - to-sm (fn [scale] (make-smeasure-nc ctx scale - (fn [g] (if (contains? (objects scale) g) g - (some (fn [o] (and (set? o) (contains? o g))) - (objects scale))))))] - (loop [n (:generations args) - generation (first-generation args ctx init-ind graph)] - (println "Generation: " (- (:generations args) n)) - (if (= n 0) - (->> generation - (apply max-key (partial fitness args ctx)) - (ind2clustered-ctx args ctx) - decode - to-sm) - (recur (dec n) (next-generation args ctx graph generation)))))) - - ;;; Declare REPL commands (defmulti run-repl-command @@ -840,7 +268,7 @@ ~doc))) (define-repl-fn done - "Ends the Scale Exploration." + "Ends the Scale Navigation." (assoc state :done true)) (define-repl-fn clear @@ -874,40 +302,55 @@ (if (empty? rename-content) state (assoc state :smeasure (apply rename-method smeasure rename-content))))) -(define-repl-fn cluster - "Apply a clustering to the scales objects or attributes." - (let [cluster-kind (ask (str "Please enter if you want to cluster attributes (:attributes) or objects (:objects): \n") - #(read-string (str (read-line))) - #(or (= :objects %) (= :attributes %)) - "The input must be :attributes or :objects: \n") - cluster-incidence (ask (str "Please enter if their common (::all) or conjoined (::ex) incidence is used as new cluster incidences: \n") - #(read-string (str (read-line))) - #(or (= ::all %) (= ::ex %)) - "The input must be ::all or ::ex: \n") - cluster-method (partial cluster cluster-kind cluster-incidence) - cluster-content (ask (str "Please enter all " (cluster-kind {:attributes "attributes" :objects "objects"}) " to be clustered with ; seperator: \n") - #(set (map read-string (clojure.string/split (str (read-line)) #";"))) - (fn [input] (println input) (every? - #(contains? ((cluster-kind {:attributes attributes :objects objects}) scale) %) - input)) - (str "Input must be ; seperated an contain only " (cluster-kind {:attributes "attributes" :objects "objects"}) " of the scale:\n"))] - (if (empty? cluster-content) state - (let [clustered (cluster-method smeasure cluster-content)] - (if (smeasure? clustered) - (assoc state :smeasure clustered) - (let [decision (ask (str "Your input does not form a valid Scale Measure. Here are some valid super-sets of your input with lowest possible cardinality: \n" - (clojure.string/join ", " - (map (partial apply str) - (seq (zipmap - (map #(str "(" % "): ") (range (count clustered))) - clustered))))"\n" - "Enter the number of one of these clusters or -1 for none of them: \n") - #(read-string (str (read-line))) - #(and (<= -1 %) (< % (count clustered))) - (str"The input must a number between -1 and " (count clustered) "\n"))] - (if (= -1 decision) - state - (assoc state :smeasure (cluster-method smeasure (nth clustered decision)))))))))) +(defn- valid-formula-level? + "Checks that every level of the formula has valid syntax." + [scale level] + (let [ops (set (filter keyword? level))] + (and (= 1 (count ops)) + (if (= :not (first ops)) + (and (= 2 (count level)) + (= :not (first level))) ; (:not attr) + (and (-> level count (> 0)) (-> level count even? not) + (->> level rest (take-nth 2) set (= ops)) ; every uneven is the operator + (->> level (take-nth 2) (every? #(or (list? %) (contains? (attributes scale) %))))))))); every even is either a formula or attributes + +(defn- formula-syntax-checker + "Checks the syntax of the input formula" + [formula scale] + (if (-> formula list? not) false + (loop [level [formula]] + (if (empty? level) true + (if (every? (partial valid-formula-level? scale) level) + (recur (filter list? formula)) + false))))) + + +(defn logical-attribute-derivation [ctx formula] + (let [incidence-ops {:or union :and intersection :not #(difference (objects ctx) %)} + op (->> formula (filter keyword?) first (get incidence-ops))] + (let [[f & other] (map #(if (list? %) % (attribute-derivation ctx #{%})) (filter (comp not keyword?) formula))] + (reduce (fn [a b] (op a (if (list? b) (logical-attribute-derivation ctx b) b))) + (-> (if (list? f) (logical-attribute-derivation ctx f) f) op) other)))) + +(define-repl-fn logical-attr + "Generates a new attribute as logical formula of existing attributes." + (let [formula (ask (str "Current Attributes: \n " (clojure.string/join " " (attributes scale)) "\n Please enter a logical formula using logical formuals e.g. \"(C :or (A :and (:not B)))\": \n ") + #(read-string (str (read-line))) + (partial formula-syntax-checker scale) + "Enter a formula in nested list format using only attributes of the scale: \n") + formula-derivation (logical-attribute-derivation scale formula) + formula-name (ask (str "Enter a name for your formula: \n ") + #(str (read-line)) + (constantly true) + "")] + (if (extent? (context (:smeasure state)) formula-derivation) + (assoc state :smeasure (make-smeasure-nc (-> state :smeasure context) + (make-context (objects scale) + (conj (attributes scale) formula-name) + (union (cross-product formula-derivation #{formula-name}) + (incidence-relation scale))) + (-> state :smeasure measure))) + state))) (define-repl-fn show "Prints the current scale context, attributes or objects." @@ -932,34 +375,23 @@ (println (str " -> " (help-repl-command cmd)))) state)) -(define-repl-fn suggest - "Suggests a scale with two dimensional concept lattice." - (let [suggestion (genetic-2d (context smeasure))] - (println suggestion) - (if (= 1 (ask "Do you wish to continue with the suggested scale? 1: yes, 0: no:" - #(read-string (str (read-line))) - (constantly true) - "")) - (assoc state :smeasure (make-smeasure-nc (context smeasure) suggestion)) - state))) - ;;; Scale Exploration -(defn scale-exploration +(defn conceptual-navigation "Exploration for a scale context to measure a given context. The exploration is done with online editing methods. - - rename: Rename objects or attributes of the scale - - cluster: Clusters objects or attributes in the scale - The cluster incidence is set as either the common - or conjoined incidences of all entries - - truncate: Removes attributes form the scale - - clear: Restarts the exploration + - rename: Rename objects or attributes of the scale + - logical-attr: Clusters objects or attributes in the scale + The cluster incidence is set as either the common + or conjoined incidences of all entries + - truncate: Removes attributes form the scale + - clear: Restarts the exploration general functions for exploration interaction - - show: prints the current scale - - done: finishes exploration - - help: prints doc string" + - show: prints the current scale + - done: finishes exploration + - help: prints doc string" [ctx] (assert (context? ctx) "Input must be a Context.") (println (:doc (meta #'scale-exploration)) "\n\n\n") From d509276fb87611252e67c0c580cbafb2d797bd08 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Mon, 26 Oct 2020 14:21:04 +0100 Subject: [PATCH 039/117] Scale-Measures Moved Logical derivations to context.clj --- src/main/clojure/conexp/fca/contexts.clj | 45 ++++++++++++++++++++++++ src/main/clojure/conexp/fca/smeasure.clj | 30 ---------------- 2 files changed, 45 insertions(+), 30 deletions(-) diff --git a/src/main/clojure/conexp/fca/contexts.clj b/src/main/clojure/conexp/fca/contexts.clj index 34e31c465..43839a4f1 100644 --- a/src/main/clojure/conexp/fca/contexts.clj +++ b/src/main/clojure/conexp/fca/contexts.clj @@ -807,6 +807,51 @@ (for [[G-H N] (concepts compatible-ctx)] (make-context-nc (difference (objects ctx) G-H) N (incidence ctx))))) +;;; logical derivations +; syntax checker +(defn- valid-formula-level? + "Checks that every level of the formula has valid syntax." + [ctx kind level] + (let [ops (set (filter keyword? level))] + (and (= 1 (count ops)) + (if (= :not (first ops)) + (and (= 2 (count level)) + (= :not (first level))) ; (:not attr) + (and (-> level count (> 0)) (-> level count even? not) + (->> level rest (take-nth 2) set (= ops)) ; every uneven is the operator + (->> level (take-nth 2) (every? #(or (list? %) (contains? (kind ctx) %))))))))); every even is either a formula or attributes + +(defn formula-syntax-checker + "Syntex checker for propositional logic. Expected Format is a list '(A :or (B :and C) (:not D)), where A,B,C,D are Attributes or Objects of ctx. + Kind is either the 'objects' or 'attributes' function." + [formula ctx kind] + (if (-> formula list? not) false + (loop [level [formula]] + (if (empty? level) true + (if (every? (partial valid-formula-level? ctx kind) level) + (recur (filter list? formula)) + false))))) +; derivations +(defn logical-object-derivation + "Returns the derivation of a propositional formula of objects. Expected Format is a list '(A :or (B :and C) (:not D)), where A,B,C,D are Objects of ctx." + [ctx formula] + (assert (formula-syntax-checker formula ctx objects) "Expected Format is a list '(A :or (B :and C) (:not D)), where A,B,C,D are Objects of the context.") + (let [incidence-ops {:or union :and intersection :not #(difference (attributes ctx) %)} + op (->> formula (filter keyword?) first (get incidence-ops))] + (let [[f & other] (map #(if (list? %) % (object-derivation ctx #{%})) (filter (comp not keyword?) formula))] + (reduce (fn [a b] (op a (if (list? b) (logical-object-derivation ctx b) b))) + (-> (if (list? f) (logical-object-derivation ctx f) f) op) other)))) + +(defn logical-attribute-derivation + "Returns the derivation of a propositional formula of objects. Expected Format is a list '(A :or (B :and C) (:not D)), where A,B,C,D are Attributes of ctx." + [ctx formula] + (assert (formula-syntax-checker formula ctx attributes) "Expected Format is a list '(A :or (B :and C) (:not D)), where A,B,C,D are Attributes of the context.") + (let [incidence-ops {:or union :and intersection :not #(difference (objects ctx) %)} + op (->> formula (filter keyword?) first (get incidence-ops))] + (let [[f & other] (map #(if (list? %) % (attribute-derivation ctx #{%})) (filter (comp not keyword?) formula))] + (reduce (fn [a b] (op a (if (list? b) (logical-attribute-derivation ctx b) b))) + (-> (if (list? f) (logical-attribute-derivation ctx f) f) op) other)))) + ;;; true diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index c7e662e92..4d5429fad 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -302,36 +302,6 @@ (if (empty? rename-content) state (assoc state :smeasure (apply rename-method smeasure rename-content))))) -(defn- valid-formula-level? - "Checks that every level of the formula has valid syntax." - [scale level] - (let [ops (set (filter keyword? level))] - (and (= 1 (count ops)) - (if (= :not (first ops)) - (and (= 2 (count level)) - (= :not (first level))) ; (:not attr) - (and (-> level count (> 0)) (-> level count even? not) - (->> level rest (take-nth 2) set (= ops)) ; every uneven is the operator - (->> level (take-nth 2) (every? #(or (list? %) (contains? (attributes scale) %))))))))); every even is either a formula or attributes - -(defn- formula-syntax-checker - "Checks the syntax of the input formula" - [formula scale] - (if (-> formula list? not) false - (loop [level [formula]] - (if (empty? level) true - (if (every? (partial valid-formula-level? scale) level) - (recur (filter list? formula)) - false))))) - - -(defn logical-attribute-derivation [ctx formula] - (let [incidence-ops {:or union :and intersection :not #(difference (objects ctx) %)} - op (->> formula (filter keyword?) first (get incidence-ops))] - (let [[f & other] (map #(if (list? %) % (attribute-derivation ctx #{%})) (filter (comp not keyword?) formula))] - (reduce (fn [a b] (op a (if (list? b) (logical-attribute-derivation ctx b) b))) - (-> (if (list? f) (logical-attribute-derivation ctx f) f) op) other)))) - (define-repl-fn logical-attr "Generates a new attribute as logical formula of existing attributes." (let [formula (ask (str "Current Attributes: \n " (clojure.string/join " " (attributes scale)) "\n Please enter a logical formula using logical formuals e.g. \"(C :or (A :and (:not B)))\": \n ") From 943262feccd4da444b9fd8e906c6661df8800798 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Thu, 10 Dec 2020 16:49:04 +0100 Subject: [PATCH 040/117] Added Scale-Measures Framework --- src/main/clojure/conexp/base.clj | 8 ++- src/main/clojure/conexp/fca/contexts.clj | 16 +++--- src/main/clojure/conexp/fca/smeasure.clj | 62 +++++++++++++++++------- 3 files changed, 60 insertions(+), 26 deletions(-) diff --git a/src/main/clojure/conexp/base.clj b/src/main/clojure/conexp/base.clj index 15f51b738..03c6e74c0 100644 --- a/src/main/clojure/conexp/base.clj +++ b/src/main/clojure/conexp/base.clj @@ -1091,5 +1091,11 @@ metadata (as provided by def) merged into the metadata of the original." (search (list [edges #{} elements 'beginning]))))) ;;; - +(defn lift-map + "This set lifts a map m:A->B to the power sets, m:P(A)->P(B)." + [m] + (let [make-set (fn [c] (if (set? c) c #{c})) + reducer-fn (fn [c d] (union (make-set c) (make-set d)))] + (fn [A] (reduce reducer-fn #{} (map m A))))) +;;; nil diff --git a/src/main/clojure/conexp/fca/contexts.clj b/src/main/clojure/conexp/fca/contexts.clj index 43839a4f1..d18e9cd2d 100644 --- a/src/main/clojure/conexp/fca/contexts.clj +++ b/src/main/clojure/conexp/fca/contexts.clj @@ -819,23 +819,23 @@ (= :not (first level))) ; (:not attr) (and (-> level count (> 0)) (-> level count even? not) (->> level rest (take-nth 2) set (= ops)) ; every uneven is the operator - (->> level (take-nth 2) (every? #(or (list? %) (contains? (kind ctx) %))))))))); every even is either a formula or attributes + (->> level (take-nth 2) (every? #(or (vector? %) (contains? (kind ctx) %))))))))); every even is either a formula or attributes (defn formula-syntax-checker - "Syntex checker for propositional logic. Expected Format is a list '(A :or (B :and C) (:not D)), where A,B,C,D are Attributes or Objects of ctx. + "Syntex checker for propositional logic. Expected Format is a list [A :or [B :and C] [:not D]], where A,B,C,D are Attributes or Objects of ctx. Kind is either the 'objects' or 'attributes' function." [formula ctx kind] - (if (-> formula list? not) false + (if (-> formula vector? not) false (loop [level [formula]] (if (empty? level) true (if (every? (partial valid-formula-level? ctx kind) level) - (recur (filter list? formula)) + (recur (reduce into [] (map (partial filter vector?) level)) ) false))))) ; derivations (defn logical-object-derivation - "Returns the derivation of a propositional formula of objects. Expected Format is a list '(A :or (B :and C) (:not D)), where A,B,C,D are Objects of ctx." + "Returns the derivation of a propositional formula of objects. Expected Format is a list [A :or [B :and C] [:not D]], where A,B,C,D are Objects of ctx." [ctx formula] - (assert (formula-syntax-checker formula ctx objects) "Expected Format is a list '(A :or (B :and C) (:not D)), where A,B,C,D are Objects of the context.") + (assert (formula-syntax-checker formula ctx objects) "Expected Format is a list [A :or [B :and C] [:not D]], where A,B,C,D are Objects of the context.") (let [incidence-ops {:or union :and intersection :not #(difference (attributes ctx) %)} op (->> formula (filter keyword?) first (get incidence-ops))] (let [[f & other] (map #(if (list? %) % (object-derivation ctx #{%})) (filter (comp not keyword?) formula))] @@ -843,9 +843,9 @@ (-> (if (list? f) (logical-object-derivation ctx f) f) op) other)))) (defn logical-attribute-derivation - "Returns the derivation of a propositional formula of objects. Expected Format is a list '(A :or (B :and C) (:not D)), where A,B,C,D are Attributes of ctx." + "Returns the derivation of a propositional formula of objects. Expected Format is a list [A :or [B :and C] [:not D]], where A,B,C,D are Attributes of ctx." [ctx formula] - (assert (formula-syntax-checker formula ctx attributes) "Expected Format is a list '(A :or (B :and C) (:not D)), where A,B,C,D are Attributes of the context.") + (assert (formula-syntax-checker formula ctx attributes) "Expected Format is a list [A :or [B :and C] [:not D]], where A,B,C,D are Attributes of the context.") (let [incidence-ops {:or union :and intersection :not #(difference (objects ctx) %)} op (->> formula (filter keyword?) first (get incidence-ops))] (let [[f & other] (map #(if (list? %) % (attribute-derivation ctx #{%})) (filter (comp not keyword?) formula))] diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 4d5429fad..6afecd997 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -112,7 +112,6 @@ ^String (smeasure-to-string sm))) ;;; - (defn- pre-image-measure "Returns the pre-image map of a scale measures function sigma." [sm] @@ -136,12 +135,19 @@ scale-extents))) + (defn valid-scale-measure? - "Checks if the input is a valid scale measure." + "Checks if the input is a valid scale measure. This check can be + performed in PTIME in the size of the context and scale by + considering attribute concepts only." [sm] - (let [pre-extents (original-extents sm)] + (let [scon (scale sm) + lifted-pre-image (lift-map (pre-image-measure sm)) + pre-attribute-extents (->> scon attributes + (map #(attribute-derivation scon #{%})) + (map lifted-pre-image))] (every? #(extent? (context sm) %) - pre-extents))) + pre-attribute-extents))) (defn smeasure? "Checks if the input is a valid scale measure." @@ -166,13 +172,30 @@ [ctx] (make-smeasure-nc ctx ctx identity)) +(defn canonical-smeasure-representation + "Given a scale-measure computes its canonical representation." + [sm] + (let [scon (scale sm) + o (original-extents sm)] + (make-smeasure-nc (context sm) (make-context (objects scon) o #(contains? %2 %1)) identity))) + +(defn logical-conjunctive-smeasure-representation + "Given a scale-measure computes the equivalent scale-measure using + logical conjunctive formulas." + [sm] + (rename-scale :attributes + (canonical-smeasure-representation sm) + (fn [a] + (rest (reduce #(conj %1 :and %2) [] + (attribute-derivation (context sm) a)))))) + (defn remove-attributes-sm "Removes 'attr attributes from the scale." [sm attr] (let [s (scale sm) new-scale (make-context (objects s) (difference (attributes s) attr) - (incidence s))] + (incidence-relation s))] (make-smeasure-nc (context sm) new-scale (measure sm)))) (defmulti rename-scale @@ -273,13 +296,13 @@ (define-repl-fn clear "Clears the current state and restarts from scratch." - (assoc state :smeasure (make-id-smeasure (context scale)))) + (assoc state :smeasure (make-id-smeasure (context smeasure)))) (define-repl-fn truncate "Enter an attribute that should be removed from the scale." (assoc state :smeasure (remove-attributes-sm smeasure - (ask (str "Please enter all to be removed attribute spereated by ';': \n") + (ask (str "Please enter all to be removed attribute spereated by ';': \n" "Current Attributes: \n " (clojure.string/join " " (attributes scale)) "\n :") #(map read-string (clojure.string/split (str (read-line)) #";")) #(subset? % (attributes scale)) "The attributes are not all present, please enter an existing attribute: \n")))) @@ -290,9 +313,10 @@ #(read-string (str (read-line))) #(or (= :objects %) (= :attributes %)) "The input must be :attributes or :objects: \n") - rename-method (partial rename rename-kind) - rename-content (ask (str "Please all " (rename-kind {:attributes "attributes" :objects "objects"}) - " that should be renamed and their new name with ; seperator (name1;new-name1;name2;...): \n") + rename-method (partial rename-scale rename-kind) + rename-content (ask (str "Please enter all " (rename-kind {:attributes "attributes" :objects "objects"}) + " that should be renamed and their new name with ; seperator (name1;new-name1;name2;...): \n" + "Current " (rename-kind {:attributes "attributes" :objects "objects"})": \n "(clojure.string/join " " ((rename-kind {:attributes attributes :objects objects}) scale))"\n") #(map read-string (clojure.string/split (str (read-line)) #";")) (fn [input] (and (even? (count input)) (every? @@ -306,7 +330,7 @@ "Generates a new attribute as logical formula of existing attributes." (let [formula (ask (str "Current Attributes: \n " (clojure.string/join " " (attributes scale)) "\n Please enter a logical formula using logical formuals e.g. \"(C :or (A :and (:not B)))\": \n ") #(read-string (str (read-line))) - (partial formula-syntax-checker scale) + #(formula-syntax-checker % scale attributes) "Enter a formula in nested list format using only attributes of the scale: \n") formula-derivation (logical-attribute-derivation scale formula) formula-name (ask (str "Enter a name for your formula: \n ") @@ -325,14 +349,18 @@ (define-repl-fn show "Prints the current scale context, attributes or objects." [state] - (let [toshow (ask (str "Please enter if you want display the scale (:context) its attributes (:attributes) or objects (:objects): \n") + (let [toshow (ask (str "Please enter if you want display the scale (:scale) or original context (:context): \n") + #(read-string (str (read-line))) + #(or (= :context %) (= :scale %)) + "The input must be :context or :scale: \n") + option (ask (str "Please enter if you want display all (:all) the objects (:objects) or the attributes (:attributes): \n") #(read-string (str (read-line))) - #(or (= :objects %) (= :attributes %) (= :context %)) - "The input must be :context, :attributes or :objects: \n")] - (println "\n" ((toshow {:context identity + #(or (= :all %) (= :objects %) (= :attributes %)) + "The input must be :attributes or :objects: \n")] + (println "\n" ((option {:all identity :attributes (comp (partial clojure.string/join "; ") attributes) :objects (comp (partial clojure.string/join "; ") objects)}) - scale)) + (toshow {:scale scale :context (context smeasure)}))) state)) (define-repl-fn help @@ -364,7 +392,7 @@ - help: prints doc string" [ctx] (assert (context? ctx) "Input must be a Context.") - (println (:doc (meta #'scale-exploration)) "\n\n\n") + (println (:doc (meta #'conceptual-navigation)) "\n\n\n") (println "Start scale exploration for:\n" ctx) (loop [state {:smeasure (make-id-smeasure ctx)}] (let [evaluated (eval-command (ask (str "Please enter an operation:\n") From e97dc7f9d8b080bfb6c4cc29f695b7165e8982b0 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Thu, 10 Dec 2020 17:56:41 +0100 Subject: [PATCH 041/117] Scale-Measure Apposition --- src/main/clojure/conexp/fca/smeasure.clj | 31 +++++++++++++------ src/main/clojure/conexp/io/smeasure.clj | 2 +- src/test/clojure/conexp/fca/contexts_test.clj | 2 +- src/test/clojure/conexp/fca/smeasure_test.clj | 29 +++-------------- 4 files changed, 28 insertions(+), 36 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 6afecd997..851e3c554 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -179,16 +179,6 @@ o (original-extents sm)] (make-smeasure-nc (context sm) (make-context (objects scon) o #(contains? %2 %1)) identity))) -(defn logical-conjunctive-smeasure-representation - "Given a scale-measure computes the equivalent scale-measure using - logical conjunctive formulas." - [sm] - (rename-scale :attributes - (canonical-smeasure-representation sm) - (fn [a] - (rest (reduce #(conj %1 :and %2) [] - (attribute-derivation (context sm) a)))))) - (defn remove-attributes-sm "Removes 'attr attributes from the scale." [sm attr] @@ -225,6 +215,27 @@ rename-fn (fn [a] (or (get rename-map a) a))] (rename-scale :attributes sm rename-fn)))) +(defn logical-conjunctive-smeasure-representation + "Given a scale-measure computes the equivalent scale-measure using + logical conjunctive formulas." + [sm] + (rename-scale :attributes + (canonical-smeasure-representation sm) + (fn [a] + (rest (reduce #(conj %1 :and %2) [] + (attribute-derivation (context sm) a)))))) + +(defn scale-apposition + [sm1 sm2] + (assert (= (context sm1) (context sm2)) "Both scale-measure must be for the same context.") + (if (and + (= (objects (scale sm1)) (objects (scale sm2))) + (= (measure sm1) (measure sm2))) + (make-smeasure-nc (context sm1) + (context-apposition (scale sm1) (scale sm2)) + (measure sm1)) + (scale-apposition (canonical-smeasure-representation sm1) + (canonical-smeasure-representation sm2)))) (derive ::all ::quant) (derive ::ex ::quant) diff --git a/src/main/clojure/conexp/io/smeasure.clj b/src/main/clojure/conexp/io/smeasure.clj index 5c65a8863..f6f213fc5 100644 --- a/src/main/clojure/conexp/io/smeasure.clj +++ b/src/main/clojure/conexp/io/smeasure.clj @@ -285,7 +285,7 @@ anchor (last (butlast (attributes ctx)))] (doall (if (>= 2 (count (str anchor))) (do -v (println (str " \\node[right = 0.45cm of ca" + (println (str " \\node[right = 0.45cm of ca" (tex-escape anchor) "] (za) {};")) (println (str " \\node[below = 0.25cm of za] (co" diff --git a/src/test/clojure/conexp/fca/contexts_test.clj b/src/test/clojure/conexp/fca/contexts_test.clj index 615789c39..3fba0a1e7 100644 --- a/src/test/clojure/conexp/fca/contexts_test.clj +++ b/src/test/clojure/conexp/fca/contexts_test.clj @@ -644,5 +644,5 @@ (some #(= some-context %) (compatible-subcontexts test-ctx-08))))) ;;; - +;(deftest logical-derivation) true diff --git a/src/test/clojure/conexp/fca/smeasure_test.clj b/src/test/clojure/conexp/fca/smeasure_test.clj index 3a2b445b8..e7d8d3cd9 100644 --- a/src/test/clojure/conexp/fca/smeasure_test.clj +++ b/src/test/clojure/conexp/fca/smeasure_test.clj @@ -44,27 +44,8 @@ (is (= (attributes (scale removed)) #{0 3 4 5})) (is (smeasure? removed)))) -(deftest test-rename - (let [ctx (rand-context (range 6) 0.5) - sm (make-id-smeasure ctx) - renamed (rename-scale-attributes - (rename-scale-objects sm 1 "test1" 2 "test2") - inc)] - (is (smeasure? renamed)))) - -(deftest test-clusterings - (let [ctx (rand-context (range 5) 0.5) - sm (make-id-smeasure ctx) - candidates (rest(subsets (range 5))) - valid-attr-cl-all (map #(cluster-attributes-all sm %) candidates) - valid-attr-cl-ex (map #(cluster-attributes-ex sm %) candidates) - valid-obj-cl-all (map #(cluster-objects-all sm %) candidates) - valid-obj-cl-ex (map #(cluster-objects-ex sm %) candidates)] - (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-all))) - (is (<= (+ 1 (count (attributes ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-all)))) - (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-ex))) - (is (<= (+ 1 (count (attributes ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-attr-cl-ex)))) - (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-all))) - (is (<= (+ 1 (count (objects ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-all)))) - (is (every? valid-scale-measure? (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-ex))) - (is (<= (+ 1 (count (objects ctx))) (count (filter #(instance? conexp.fca.smeasure.ScaleMeasure %) valid-obj-cl-ex)))))) +;(deftest rename-scale) +;(deftest logical-conjunctive-smeasure-representation) +;(deftest scale-apposition) +;(deftest remove-attributes sm) +;(deftest scale-measure?) From 6dd2ec36d164255286bcab6aad30e826f822601e Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Fri, 18 Dec 2020 12:27:15 +0100 Subject: [PATCH 042/117] Recommend based on an importance measure --- src/main/clojure/conexp/fca/smeasure.clj | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 851e3c554..62db45aba 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -237,6 +237,29 @@ (scale-apposition (canonical-smeasure-representation sm1) (canonical-smeasure-representation sm2)))) +(defn recommend-by-importance + "Recommends a scale-measure reflecting the 'n most important + concepts based on a concept importance measure. + Some importance measures are: + - stability: conexp.fca.metrics/concept-stability + - separation index: conexp.fca.metrics/concept-separation + - probability: conexp.fca.metrics/concept-probability + - robustness: (fn [context concept] + (conexp.fca.metrics/concept-robustness + concept (concepts context) your-alpha your-sorted?)) + - support: (fn [context concept] (count (first concept)))" + [context imp-fn n] + (let [dual (dual-context context) ;; measure importance for extents + imp-n-concepts (take-last n + (sort-by (partial imp-fn dual) + (concepts dual))) + exts (map last imp-n-concepts) + scale (make-context (objects context) exts + (fn [a b] (contains? b a)))] + (println "The " n " most important extents produced " + (-> scale extents count) " concepts.") + (make-smeasure-nc context scale identity))) + (derive ::all ::quant) (derive ::ex ::quant) From 1282a086d6f2ae4d1ffb9c09a08a0a70ef7b2cce Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Mon, 21 Dec 2020 11:47:21 +0100 Subject: [PATCH 043/117] Added scale-measure exploration and recommendation by importance measures --- src/main/clojure/conexp/fca/smeasure.clj | 98 +++++++++++++++++++++++- 1 file changed, 95 insertions(+), 3 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 62db45aba..9200d1924 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -13,7 +13,8 @@ [conexp.fca.cover :refer [generate-concept-cover]] [clojure.math.combinatorics :as comb] [loom.graph :as lg] [loom.alg :as la] - [clojure.core.reducers :as r])) + [clojure.core.reducers :as r] + [conexp.fca.implications :refer :all])) (defprotocol Smeasure (context [sm] "Returns the original context that is measured.") @@ -252,7 +253,7 @@ (let [dual (dual-context context) ;; measure importance for extents imp-n-concepts (take-last n (sort-by (partial imp-fn dual) - (concepts dual))) + (rest (concepts dual)))) exts (map last imp-n-concepts) scale (make-context (objects context) exts (fn [a b] (contains? b a)))] @@ -264,7 +265,7 @@ (derive ::ex ::quant) -;;; Declare REPL commands +;;; Declare REPL commandso (defmulti run-repl-command "Runs a command for the counterexample REPL." (fn [& args] (first args))) @@ -436,3 +437,94 @@ (if (:done evaluated) (:smeasure evaluated) (recur evaluated))))) + + +(defn- provide-counter-example + "Queries for a counter example B and applies the closure operator of + the context of the explored scale-measure. This ensures that + reflected set of extents is a subset of the contexts extents." + [state cur cur-conclusion] + (let [premise-deri (object-derivation (:context state) cur) + concl-deri (object-derivation (:context state) cur-conclusion) + deri-margin (difference premise-deri concl-deri) + counter (ask (str "Please enter by you allow coarsening of objects having additional:\n" deri-margin "\n down to only " concl-deri + " you allow\n Enter a subset of " deri-margin " that will be neglected:\n Note that if the closure of your input \n and the later attribute set is has all mentioned \n attributes, you end up in an infinite loop until \n you enter a proper subset:\n") + #(let [input (str (read-line))] + (if (= "" input) #{} + (set (map read-string + (clojure.string/split input #";"))))) + #(subset? % deri-margin) + (str "The input must be a subset of " deri-margin ":\n")) + counter-cl (context-attribute-closure (:context state) (union concl-deri counter))] + (if (ask (str "You entered " counter " with closure " counter-cl "\n Do you want to apply the coarsoning of " + deri-margin " down to " (difference counter-cl concl-deri) "?\n") + #(read-string (str (read-line))) + #(or (= true %) (= % false)) + "Enter true or false:\n") + (attribute-derivation (:context state) (union concl-deri counter)) + (provide-counter-example state cur cur-conclusion)))) + +(defn- coarsened-by-imp? + "Queries a boolean if an implication should used in the scale-measure + exploration." + [state cur cur-conclusion] + (let [premise-deri (object-derivation (:context state) cur) + concl-deri (object-derivation (:context state) cur-conclusion) + deri-margin (difference premise-deri concl-deri) + answer (ask (str "Do you allow neglection of " deri-margin + " for object having " concl-deri "?\n Enter true or false:") + #(read-string (str (read-line))) + #(or (= true %) (= % false)) + "Enter true or false:\n")] + answer)) + +(defn- exploration-of-scales-iteration + "This is method performs each iteration of the scale-measure + exploration to determine an object set B to coarsen a context by the + object implication cur->B with B beeing a subset of + cur-conclusion. This is done by querying sets B until a suggested + implication holds and no B is provided. Then the next iteration can + be called with the next-closured set of cur." + [state] + (loop [cur-conclusion (context-object-closure (:scale state) (:cur state)) iter-state state] + (if (= cur-conclusion (:cur iter-state)) + (let [next-cur (next-closed-set (:object-order iter-state) + (clop-by-implications (:imps iter-state)) + (:cur iter-state))] + (assoc iter-state :cur next-cur)) + (let [coarse? (coarsened-by-imp? iter-state (:cur iter-state) cur-conclusion)] + (if coarse? + (let [new-imps (conj (:imps iter-state) (make-implication (:cur iter-state) cur-conclusion)) + next-cur (next-closed-set (:object-order iter-state) + (clop-by-implications new-imps) + (:cur iter-state))] + (-> iter-state + (assoc :imps new-imps) + (assoc :cur next-cur))) + (let [counter (provide-counter-example iter-state (:cur iter-state) cur-conclusion) + state-with-counter + (update iter-state :scale + #(make-context (objects %) + (conj (attributes %) + counter) + (:inc state)))] + (recur (context-object-closure (:scale state-with-counter) (:cur state-with-counter)) + state-with-counter))))))) + +(defn exploration-of-scales + "This algorithm performs an object-exploration with background + knowledge (context) to determine a scale-measure." + [context] + (let [object-order (-> context objects vec) + incidence-fn (fn ([a b] (contains? b a)) + ([[a b]] (contains? b a))) + init-scale (make-context object-order #{} incidence-fn)] + (loop [state {:scale init-scale :cur #{} :imps (canonical-base + context) :inc incidence-fn :context context :object-order + object-order}] + (if (= (objects context) + (:cur state)) + (make-smeasure-nc context (:scale state) identity) + (recur (exploration-of-scales-iteration state)))))) + + From 8b98c0b50559aeee0a47215b974d1021e10aa2c8 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Mon, 21 Dec 2020 17:05:50 +0100 Subject: [PATCH 044/117] Only meet-irreducible scale-measure attributes --- src/main/clojure/conexp/fca/smeasure.clj | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 9200d1924..d3a81ac5b 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -216,7 +216,7 @@ rename-fn (fn [a] (or (get rename-map a) a))] (rename-scale :attributes sm rename-fn)))) -(defn logical-conjunctive-smeasure-representation +(defn conjunctive-normalform-smeasure-representation "Given a scale-measure computes the equivalent scale-measure using logical conjunctive formulas." [sm] @@ -247,7 +247,7 @@ - probability: conexp.fca.metrics/concept-probability - robustness: (fn [context concept] (conexp.fca.metrics/concept-robustness - concept (concepts context) your-alpha your-sorted?)) + concept (concepts context) your-alpha)) - support: (fn [context concept] (count (first concept)))" [context imp-fn n] (let [dual (dual-context context) ;; measure importance for extents From a716a6e3f31a2b8fe7c4520cb80f6c75acf63e2b Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Fri, 8 Jan 2021 16:21:20 +0100 Subject: [PATCH 045/117] More intuitive questionary + Minor Bug fix --- src/main/clojure/conexp/fca/smeasure.clj | 102 +++++++++++++---------- 1 file changed, 59 insertions(+), 43 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index d3a81ac5b..1be7d6eeb 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -216,6 +216,11 @@ rename-fn (fn [a] (or (get rename-map a) a))] (rename-scale :attributes sm rename-fn)))) +(defn meet-irreducibles-only-smeasure + "Removes all non meet-irreducible attributes from the scale-measure." + [sm] + (make-smeasure-nc (context sm) (-> sm scale reduce-attributes) (measure sm))) + (defn conjunctive-normalform-smeasure-representation "Given a scale-measure computes the equivalent scale-measure using logical conjunctive formulas." @@ -224,7 +229,7 @@ (canonical-smeasure-representation sm) (fn [a] (rest (reduce #(conj %1 :and %2) [] - (attribute-derivation (context sm) a)))))) + (object-derivation (context sm) a)))))) (defn scale-apposition [sm1 sm2] @@ -447,8 +452,9 @@ (let [premise-deri (object-derivation (:context state) cur) concl-deri (object-derivation (:context state) cur-conclusion) deri-margin (difference premise-deri concl-deri) - counter (ask (str "Please enter by you allow coarsening of objects having additional:\n" deri-margin "\n down to only " concl-deri - " you allow\n Enter a subset of " deri-margin " that will be neglected:\n Note that if the closure of your input \n and the later attribute set is has all mentioned \n attributes, you end up in an infinite loop until \n you enter a proper subset:\n") + counter (ask (str "Have: " concl-deri "\n how much more of " deri-margin + " \n do you want? \n Enter a subset of " + deri-margin ":\n Note that the empty input will result in an infinite loop\n") #(let [input (str (read-line))] (if (= "" input) #{} (set (map read-string @@ -456,11 +462,10 @@ #(subset? % deri-margin) (str "The input must be a subset of " deri-margin ":\n")) counter-cl (context-attribute-closure (:context state) (union concl-deri counter))] - (if (ask (str "You entered " counter " with closure " counter-cl "\n Do you want to apply the coarsoning of " - deri-margin " down to " (difference counter-cl concl-deri) "?\n") - #(read-string (str (read-line))) - #(or (= true %) (= % false)) - "Enter true or false:\n") + (if (= "yes" (ask (str "You entered " counter " with closure " counter-cl "\n Please confirm with yes or no:\n") + #(str (read-line)) + #(or (= "yes" %) (= % "no")) + "Enter yes or no:\n")) (attribute-derivation (:context state) (union concl-deri counter)) (provide-counter-example state cur cur-conclusion)))) @@ -471,14 +476,14 @@ (let [premise-deri (object-derivation (:context state) cur) concl-deri (object-derivation (:context state) cur-conclusion) deri-margin (difference premise-deri concl-deri) - answer (ask (str "Do you allow neglection of " deri-margin - " for object having " concl-deri "?\n Enter true or false:") - #(read-string (str (read-line))) - #(or (= true %) (= % false)) - "Enter true or false:\n")] + answer (ask (str "Have: " concl-deri + " want more of " deri-margin "?\n Enter yes, none or all:\n") + #(str (read-line)) + #(or (= "none" %) (= % "all") (= "yes" %) (= % "no")) + "Enter yes, all or none :\n")] answer)) -(defn- exploration-of-scales-iteration +(defn exploration-of-scales-iteration "This is method performs each iteration of the scale-measure exploration to determine an object set B to coarsen a context by the object implication cur->B with B beeing a subset of @@ -487,44 +492,55 @@ be called with the next-closured set of cur." [state] (loop [cur-conclusion (context-object-closure (:scale state) (:cur state)) iter-state state] + (println (:cur iter-state) cur-conclusion) (if (= cur-conclusion (:cur iter-state)) (let [next-cur (next-closed-set (:object-order iter-state) (clop-by-implications (:imps iter-state)) (:cur iter-state))] (assoc iter-state :cur next-cur)) (let [coarse? (coarsened-by-imp? iter-state (:cur iter-state) cur-conclusion)] - (if coarse? - (let [new-imps (conj (:imps iter-state) (make-implication (:cur iter-state) cur-conclusion)) - next-cur (next-closed-set (:object-order iter-state) - (clop-by-implications new-imps) - (:cur iter-state))] - (-> iter-state - (assoc :imps new-imps) - (assoc :cur next-cur))) - (let [counter (provide-counter-example iter-state (:cur iter-state) cur-conclusion) - state-with-counter - (update iter-state :scale - #(make-context (objects %) - (conj (attributes %) - counter) - (:inc state)))] - (recur (context-object-closure (:scale state-with-counter) (:cur state-with-counter)) - state-with-counter))))))) + (cond ; not wanting attributes means cur should be closed. Hence add all attributes in the question + ; all attributes are already closed. will could result in endless loop + (= coarse? "none") (let [closed-premise + (update iter-state :scale + #(make-context (objects %) + (conj (attributes %) + (:cur iter-state)) + (:inc state)))] + (recur (context-object-closure (:scale closed-premise) (:cur closed-premise)) + closed-premise)) + (= coarse? "yes") (let [counter (provide-counter-example iter-state (:cur iter-state) cur-conclusion) + state-with-counter + (update iter-state :scale + #(make-context (objects %) + (conj (attributes %) + counter) + (:inc state)))] + (recur (context-object-closure (:scale state-with-counter) (:cur state-with-counter)) + state-with-counter)) + (= coarse? "all") (let [new-imps (conj (:imps iter-state) (make-implication (:cur iter-state) cur-conclusion)) + next-cur (next-closed-set (:object-order iter-state) + (clop-by-implications new-imps) + (:cur iter-state))] + (-> iter-state + (assoc :imps new-imps) + (assoc :cur next-cur)))))))) (defn exploration-of-scales "This algorithm performs an object-exploration with background knowledge (context) to determine a scale-measure." - [context] - (let [object-order (-> context objects vec) - incidence-fn (fn ([a b] (contains? b a)) - ([[a b]] (contains? b a))) - init-scale (make-context object-order #{} incidence-fn)] - (loop [state {:scale init-scale :cur #{} :imps (canonical-base - context) :inc incidence-fn :context context :object-order - object-order}] - (if (= (objects context) - (:cur state)) - (make-smeasure-nc context (:scale state) identity) - (recur (exploration-of-scales-iteration state)))))) + ([context] + (exploration-of-scales context (-> context objects vec))) + ([context object-order] + (let [incidence-fn (fn ([a b] (contains? b a)) + ([[a b]] (contains? b a))) + init-scale (make-context object-order #{} incidence-fn)] + (loop [state {:scale init-scale :cur #{} :object-order object-order + :imps (canonical-base (dual-context context)) + :inc incidence-fn :context context }] + (if (= (objects context) + (:cur state)) + (make-smeasure-nc context (:scale state) identity) + (recur (exploration-of-scales-iteration state))))))) From de8d882bbb784272066d1333069708b30ebaf5b3 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Fri, 5 Feb 2021 12:47:06 +0100 Subject: [PATCH 046/117] smeasures: updated questionary --- src/main/clojure/conexp/fca/smeasure.clj | 23 +++++++++++++---------- 1 file changed, 13 insertions(+), 10 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 1be7d6eeb..e02d72b04 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -462,12 +462,14 @@ #(subset? % deri-margin) (str "The input must be a subset of " deri-margin ":\n")) counter-cl (context-attribute-closure (:context state) (union concl-deri counter))] - (if (= "yes" (ask (str "You entered " counter " with closure " counter-cl "\n Please confirm with yes or no:\n") + (let [answer (ask (str "You entered " counter " with closure " counter-cl "\n Please confirm with yes or no:") #(str (read-line)) #(or (= "yes" %) (= % "no")) - "Enter yes or no:\n")) - (attribute-derivation (:context state) (union concl-deri counter)) - (provide-counter-example state cur cur-conclusion)))) + "\n Enter yes or no:")] + (println answer "\n") + (if (= "yes" answer) + (attribute-derivation (:context state) (union concl-deri counter)) + (provide-counter-example state cur cur-conclusion))))) (defn- coarsened-by-imp? "Queries a boolean if an implication should used in the scale-measure @@ -477,10 +479,11 @@ concl-deri (object-derivation (:context state) cur-conclusion) deri-margin (difference premise-deri concl-deri) answer (ask (str "Have: " concl-deri - " want more of " deri-margin "?\n Enter yes, none or all:\n") + " want more of " deri-margin "?\n Enter yes, none or all:") #(str (read-line)) #(or (= "none" %) (= % "all") (= "yes" %) (= % "no")) - "Enter yes, all or none :\n")] + "\n Enter yes, all or none :")] + (println answer "\n") answer)) (defn exploration-of-scales-iteration @@ -492,7 +495,7 @@ be called with the next-closured set of cur." [state] (loop [cur-conclusion (context-object-closure (:scale state) (:cur state)) iter-state state] - (println (:cur iter-state) cur-conclusion) + ;(println (:cur iter-state) cur-conclusion) print object implication (if (= cur-conclusion (:cur iter-state)) (let [next-cur (next-closed-set (:object-order iter-state) (clop-by-implications (:imps iter-state)) @@ -501,7 +504,7 @@ (let [coarse? (coarsened-by-imp? iter-state (:cur iter-state) cur-conclusion)] (cond ; not wanting attributes means cur should be closed. Hence add all attributes in the question ; all attributes are already closed. will could result in endless loop - (= coarse? "none") (let [closed-premise + (= coarse? "all") (let [closed-premise (update iter-state :scale #(make-context (objects %) (conj (attributes %) @@ -518,8 +521,8 @@ (:inc state)))] (recur (context-object-closure (:scale state-with-counter) (:cur state-with-counter)) state-with-counter)) - (= coarse? "all") (let [new-imps (conj (:imps iter-state) (make-implication (:cur iter-state) cur-conclusion)) - next-cur (next-closed-set (:object-order iter-state) + (= coarse? "none") (let [new-imps (conj (:imps iter-state) (make-implication (:cur iter-state) cur-conclusion)) + next-cur (next-closed-set (:object-order iter-state) (clop-by-implications new-imps) (:cur iter-state))] (-> iter-state From ab1730a8266db1157744f08b28fd424fd1f45fad Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 25 May 2021 09:51:51 +0200 Subject: [PATCH 047/117] Scaling error --- src/main/clojure/conexp/fca/smeasure.clj | 90 ++++++++++++++++++++++++ 1 file changed, 90 insertions(+) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index e02d72b04..c9d4e5aa1 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -11,6 +11,8 @@ [conexp.fca.contexts :refer :all] [conexp.fca.concept-transform :refer :all] [conexp.fca.cover :refer [generate-concept-cover]] + [conexp.fca.lattices :refer [concept-lattice + lattice-inf-irreducibles]] [clojure.math.combinatorics :as comb] [loom.graph :as lg] [loom.alg :as la] [clojure.core.reducers :as r] @@ -126,6 +128,14 @@ (apply (partial merge-with into) {} (for [[k v] mapified] {v #{k}})))))) +(defn- lifted-pre-image-measure + "Returns the pre-image map as function on the power set of G of a + scale measures function sigma." + [sm] + (let [m (pre-image-measure sm)] + (fn [scale-objs] + (set (reduce into (map m scale-objs)))))) + (defn original-extents "Returns the pre-image of all extents whichs image is closed in the scale." @@ -173,6 +183,15 @@ [ctx] (make-smeasure-nc ctx ctx identity)) +(defn smeasure-by-exts + "Returns the canonical scale-measure which reflects exts." + [cxt exts] + (make-smeasure-nc cxt + (make-context (objects cxt) + exts + #(contains? %2 %1)) + identity)) + (defn canonical-smeasure-representation "Given a scale-measure computes its canonical representation." [sm] @@ -180,6 +199,47 @@ o (original-extents sm)] (make-smeasure-nc (context sm) (make-context (objects scon) o #(contains? %2 %1)) identity))) +(defn join-complement + "Returns the canonical representation of the join-complement of sm in the scale-hierarchy." + [sm] + (let [cxt (context sm) + s (scale sm) + m (measure sm) + join-complement-scale (make-context (objects cxt) + (difference (->> cxt concept-lattice + lattice-inf-irreducibles + (map first) + set) + (-> sm original-extents + set)) + #(contains? %2 %1))] + (canonical-smeasure-representation + (make-smeasure-nc cxt join-complement-scale identity)))) + +(defn error-in-smeasure + "Returns all false reflected extents." + ([sm] + (->> sm + original-extents + (filter #(not (extent? (context sm) %))))) + ([cxt s m] + (error-in-smeasure (make-smeasure-nc cxt s m)))) + +(defn valid-attributes + "Returns all attributes of the scale whichs derivation pre-image is an + extents of cxt." + ([sm] + (valid-attributes (context sm) + (scale sm) + (measure sm))) + ([cxt s m] + (let [pre-image (lifted-pre-image-measure (make-smeasure-nc cxt s m))] + (filter #(->> #{%} + (attribute-derivation s) + pre-image + (extent? cxt)) + (attributes s))))) + (defn remove-attributes-sm "Removes 'attr attributes from the scale." [sm attr] @@ -189,6 +249,36 @@ (incidence-relation s))] (make-smeasure-nc (context sm) new-scale (measure sm)))) +(defn smeasure-valid-attr + "Filters the scale-measure scale attributes to the set of valid attributes." + [sm] + (let [inval-attr (difference (-> sm scale attributes) + (valid-attributes sm))] + (remove-attributes-sm sm inval-attr))) + +(defn smeasure-invalid-attr + "Filters the scale-measure scale attributes to the set of valid attributes." + [sm] + (let [val-attr (valid-attributes sm)] + (remove-attributes-sm sm val-attr))) + + + +(defn smeasure-valid-exts + "Filters the scale-measure scale attributes to the set of valid attributes." + [sm] + (let [invalid-exts (error-in-smeasure sm) ] + (smeasure-by-exts (context sm) + (difference (-> sm context extents set) + (set invalid-exts))))) + +(defn smeasure-invalid-exts + "Filters the scale-measure scale attributes to the set of valid attributes." + [sm] + (let [invalid-exts (error-in-smeasure sm) ] + (smeasure-by-exts (context sm) + (set invalid-exts)))) + (defmulti rename-scale "Renames objects or attributes in the scale. Input the renaming as function on the set of objects or as key value pairs." From 09515e5d81381af2209f5261b2e23baa8a3235a0 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Wed, 21 Jul 2021 14:36:11 +0200 Subject: [PATCH 048/117] Resolved Merge --- src/main/clojure/conexp/fca/cover.clj | 118 +++++++++++++------------- 1 file changed, 59 insertions(+), 59 deletions(-) diff --git a/src/main/clojure/conexp/fca/cover.clj b/src/main/clojure/conexp/fca/cover.clj index 521ac230f..d2c22064b 100644 --- a/src/main/clojure/conexp/fca/cover.clj +++ b/src/main/clojure/conexp/fca/cover.clj @@ -7,15 +7,15 @@ ;; You must not remove this notice, or any other, from this software. (ns conexp.fca.cover - (:require [conexp.base :refer :all] - ; :exclude [next-closed-set]] + (:require [conexp.base :refer :all + :exclude [next-closed-set]] [conexp.fca.contexts :refer :all] [conexp.fca.fast :refer [next-intent-async - ;next-closed-set + next-closed-set to-hashset to-binary-context - ;bitwise-attribute-derivation - ;bitwise-object-derivation + bitwise-attribute-derivation + bitwise-object-derivation to-binary-matrix bitwise-context-attribute-closure]] [clojure.core.reducers :as r] @@ -337,50 +337,6 @@ (add-to-cover intent (find-lower-neighbors inserted root intent)))) intent #(assoc % :extent extent)))) -;; (defn attribute-insertion-cover -;; "This method updates the concept lattice given by cover on an -;; insertion of attributes to the context. The added attributes are -;; already included in new-context and are further given by -;; new-attributes." -;; [cover new-ctx new-attributes] -;; (if (empty? new-attributes) cover -;; (let [prev-attributes (difference -;; (attributes new-ctx) -;; new-attributes) -;; attr-order (into -;; (vec new-attributes) -;; (vec prev-attributes)) -;; obj-vec (vec (objects new-ctx)) -;; bin-incidence (to-binary-matrix obj-vec attr-order -;; (fn ([a b] ((incidence new-ctx) [a b])) -;; ([[a b]] ((incidence new-ctx) [a b])))) -;; bin-ctx [obj-vec attr-order (count obj-vec) (count attr-order) bin-incidence] -;; start (BitSet.) -;; setter (.set start (count new-attributes) (count attr-order) true) -;; cur-lattice (agent cover) -;; bin-first-next (next-closed-set-iterator bin-ctx start)] -;; (if (nil? bin-first-next) cover -;; (loop [next (to-hashset attr-order bin-first-next) bin-next bin-first-next] -;; (let [old (intersection next prev-attributes)] -;; ;; async update cover -;; (send-off cur-lattice insert-concept next (attribute-derivation new-ctx next)) - -;; (send-off cur-lattice -;; #(if (= old -;; (to-hashset attr-order -;; (let [n (.clone bin-next) oldn (.and n start)] -;; (bitwise-context-attribute-closure -;; bin-incidence -;; (count obj-vec) -;; (count attr-order) -;; n)))) -;; % -;; (reassign-cover % old))) -;; (if (= next (attributes new-ctx)) -;; (do (await cur-lattice) @cur-lattice) -;; (let [bin-closure (next-closed-set-iterator bin-ctx bin-next)] -;; (recur (to-hashset attr-order bin-closure) bin-closure))))))))) - (defn attribute-insertion-cover "This method updates the concept lattice given by cover on an insertion of attributes to the context. The added attributes are @@ -388,19 +344,63 @@ new-attributes." [cover new-ctx new-attributes] (if (empty? new-attributes) cover - (let [intent-chan (next-intent-async new-ctx new-attributes :exlusive) - prev-attributes (difference + (let [prev-attributes (difference (attributes new-ctx) new-attributes) - cur-lattice (agent cover)] - (loop [next-intent ( Date: Wed, 21 Jul 2021 14:37:05 +0200 Subject: [PATCH 049/117] Added comment for cover method --- src/main/clojure/conexp/fca/cover.clj | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/main/clojure/conexp/fca/cover.clj b/src/main/clojure/conexp/fca/cover.clj index d2c22064b..0f2156ec2 100644 --- a/src/main/clojure/conexp/fca/cover.clj +++ b/src/main/clojure/conexp/fca/cover.clj @@ -380,7 +380,7 @@ (do (await cur-lattice) @cur-lattice) (let [bin-closure (next-closed-set-iterator bin-ctx bin-next)] (recur (to-hashset attr-order bin-closure) bin-closure))))))))) - +;; Variation without fast implementation ;; (defn attribute-insertion-cover ;; "This method updates the concept lattice given by cover on an ;; insertion of attributes to the context. The added attributes are From 1bc1004e039393bcb11101513d51b0fa09103299 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Wed, 8 Dec 2021 14:29:01 +0100 Subject: [PATCH 050/117] meet and join operator --- src/main/clojure/conexp/fca/smeasure.clj | 60 +++++++++++++++++++----- 1 file changed, 48 insertions(+), 12 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index c9d4e5aa1..1a7bf52bf 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -199,6 +199,54 @@ o (original-extents sm)] (make-smeasure-nc (context sm) (make-context (objects scon) o #(contains? %2 %1)) identity))) +(defn scale-apposition + [sm1 sm2] + (assert (= (context sm1) (context sm2)) "Both scale-measure must be for the same context.") + (if (and + (= (objects (scale sm1)) (objects (scale sm2))) + (= (measure sm1) (measure sm2))) + (make-smeasure-nc (context sm1) + (context-apposition (scale sm1) (scale sm2)) + (measure sm1)) + (scale-apposition (canonical-smeasure-representation sm1) + (canonical-smeasure-representation sm2)))) + +(defn scale-apposition + [sm1 sm2] + (assert (= (context sm1) (context sm2)) "Both scale-measure must be for the same context.") + (if (and + (= (objects (scale sm1)) (objects (scale sm2))) + (= (measure sm1) (measure sm2))) + (make-smeasure-nc (context sm1) + (context-apposition (scale sm1) (scale sm2)) + (measure sm1)) + (scale-apposition (canonical-smeasure-representation sm1) + (canonical-smeasure-representation sm2)))) + +(alias 'join-smeasure 'scale-apposition) + +(defn meet-smeasure + "Returns the canonical representation of the join-complement of sm in the scale-hierarchy." + [sm1 sm2] + (assert (= (context sm1) (context sm2)) "Both scale-measure must be for the same context.") + (smeasure-by-exts (context sm1) + (intersection (set (original-extents sm1)) + (set (original-extents sm1)))) +;;;;;;;;; + (let [cxt (context sm) + s (scale sm) + m (measure sm) + join-complement-scale (make-context (objects cxt) + (difference (->> cxt concept-lattice + lattice-inf-irreducibles + (map first) + set) + (-> sm original-extents + set)) + #(contains? %2 %1))] + (canonical-smeasure-representation + (make-smeasure-nc cxt join-complement-scale identity)))) + (defn join-complement "Returns the canonical representation of the join-complement of sm in the scale-hierarchy." [sm] @@ -321,18 +369,6 @@ (rest (reduce #(conj %1 :and %2) [] (object-derivation (context sm) a)))))) -(defn scale-apposition - [sm1 sm2] - (assert (= (context sm1) (context sm2)) "Both scale-measure must be for the same context.") - (if (and - (= (objects (scale sm1)) (objects (scale sm2))) - (= (measure sm1) (measure sm2))) - (make-smeasure-nc (context sm1) - (context-apposition (scale sm1) (scale sm2)) - (measure sm1)) - (scale-apposition (canonical-smeasure-representation sm1) - (canonical-smeasure-representation sm2)))) - (defn recommend-by-importance "Recommends a scale-measure reflecting the 'n most important concepts based on a concept importance measure. From 0983fd2ee8cff4e4052a6f2aa64a2925a77032a4 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Wed, 8 Dec 2021 14:35:59 +0100 Subject: [PATCH 051/117] Bugfix --- src/main/clojure/conexp/fca/smeasure.clj | 18 ++---------------- 1 file changed, 2 insertions(+), 16 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 1a7bf52bf..59960e5c7 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -223,7 +223,7 @@ (scale-apposition (canonical-smeasure-representation sm1) (canonical-smeasure-representation sm2)))) -(alias 'join-smeasure 'scale-apposition) +(defalias join-smeasure scale-apposition) (defn meet-smeasure "Returns the canonical representation of the join-complement of sm in the scale-hierarchy." @@ -231,21 +231,7 @@ (assert (= (context sm1) (context sm2)) "Both scale-measure must be for the same context.") (smeasure-by-exts (context sm1) (intersection (set (original-extents sm1)) - (set (original-extents sm1)))) -;;;;;;;;; - (let [cxt (context sm) - s (scale sm) - m (measure sm) - join-complement-scale (make-context (objects cxt) - (difference (->> cxt concept-lattice - lattice-inf-irreducibles - (map first) - set) - (-> sm original-extents - set)) - #(contains? %2 %1))] - (canonical-smeasure-representation - (make-smeasure-nc cxt join-complement-scale identity)))) + (set (original-extents sm1))))) (defn join-complement "Returns the canonical representation of the join-complement of sm in the scale-hierarchy." From d9da95718172716a8b663f901bb457d00a44c52f Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 25 Jan 2022 15:49:08 +0100 Subject: [PATCH 052/117] Added a relative scaling errors --- src/main/clojure/conexp/fca/smeasure.clj | 34 ++++++++++++++++++++++++ 1 file changed, 34 insertions(+) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 59960e5c7..7fdacadd5 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -274,6 +274,40 @@ (extent? cxt)) (attributes s))))) +(defn invalid-attributes + "Returns all attributes of the scale whichs derivation pre-image is + not an extents of cxt." + ([sm] + (valid-attributes (context sm) + (scale sm) + (measure sm))) + ([cxt s m] + (let [v (valid-attributes cxt s m)] + (difference (attributes s) v)))) + +(defn conceptual-scaling-error + "Computes the conceptual scaling error, i.e., the number of falsely + reflected extents by the scaling sm. + DOI:https://doi.org/10.1007/978-3-030-86982-3_8" + ([sm & {:keys [relative] :or {relative false}}] + (let [o (original-extents sm) + error (count (filter #(not (extent? (context sm) %))))] + (if relative + (/ (count error) (count o)) + (count error))))) + +(defn attribute-scaling-error + "Computes the attribute scaling error, i.e., the number attributes that + induce an inconsistent data scaling. This score is an approximation of + the conceptual scaling error. + DOI:https://doi.org/10.1007/978-3-030-86982-3_8 " + ([sm & {:keys [relative] :or {relative false}}] + (let [a (-> sm scale attributes) + error (-> sm invalid-attributes count)] + (if relative + (/ (count error) (count a)) + (count error))))) + (defn remove-attributes-sm "Removes 'attr attributes from the scale." [sm attr] From 66c2ab42a5cfd92574aeefe1eb92b368eb2ebc4e Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Mon, 21 Feb 2022 17:29:28 +0100 Subject: [PATCH 053/117] Compute all concepts containing g and their covering --- src/main/clojure/conexp/fca/contexts.clj | 12 ++++++++++-- src/main/clojure/conexp/fca/smeasure.clj | 24 +++++++++++++++++++++++- 2 files changed, 33 insertions(+), 3 deletions(-) diff --git a/src/main/clojure/conexp/fca/contexts.clj b/src/main/clojure/conexp/fca/contexts.clj index f51ac566e..36e6b43ed 100644 --- a/src/main/clojure/conexp/fca/contexts.clj +++ b/src/main/clojure/conexp/fca/contexts.clj @@ -767,7 +767,11 @@ (defn direct-upper-concepts "Computes the set of direct upper neighbours of the concept [A B] in - the concept lattice of ctx. Uses Lindig's Algorithm for that." + the concept lattice of ctx. Uses Lindig's Algorithm for that. + + Lindig, C.: Fast concept analysis. In: Working with Conceptual + Structures – Contributions to ICCS 2000. pp. 152--161. Shaker + Verlag (2000). " [ctx [A B]] (assert (concept? ctx [A B]) "Given pair must a concept in the given context") @@ -791,7 +795,11 @@ (defn direct-lower-concepts "Computes the set of direct upper neighbours of the concept [A B] in - the concept lattice of ctx. Uses Lindig's Algorithm for that." + the concept lattice of ctx. Uses Lindig's Algorithm for that. + + Lindig, C.: Fast concept analysis. In: Working with Conceptual + Structures – Contributions to ICCS 2000. pp. 152--161. Shaker + Verlag (2000). " [ctx [A B]] (assert (concept? ctx [A B]) "Given pair must a concept in the given context") diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index c9d4e5aa1..78394a10c 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -636,4 +636,26 @@ (make-smeasure-nc context (:scale state) identity) (recur (exploration-of-scales-iteration state))))))) - +;;;;;;;;;;;;;;; local scaling for a single object + +;; Computes all concepts containing an object g and the concepts in covering relation + +(defn concept-lattice-filter+covering-concepts + "Computes all concepts containing object g and their covering + concepts." + [ctx g] + (let [first-C [(attribute-derivation ctx #{}) + (context-attribute-closure ctx #{})]] + (loop [BV #{first-C} + queue #{first-C}] + (if (empty? queue) + BV + (let [C (first queue)] + (let [covering-C (direct-lower-concepts ctx C) + ;; those not containing g can be added since they are in cover with a concept containing c + out (println "out " covering-C) + new-C (difference covering-C BV) + ;; only continue with those that contain g to ensure selection criteria + for-queue (filter #(contains? (first %) g) new-C) + out (println "queue " for-queue)] + (recur (into BV new-C) (into (disj queue C) for-queue)))))))) From 33c4601bd449a58d2ff0827b3bf9d5a6442a3d2f Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 22 Feb 2022 11:14:16 +0100 Subject: [PATCH 054/117] Removed prints --- src/main/clojure/conexp/fca/smeasure.clj | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/src/main/clojure/conexp/fca/smeasure.clj b/src/main/clojure/conexp/fca/smeasure.clj index 78394a10c..8ed036671 100644 --- a/src/main/clojure/conexp/fca/smeasure.clj +++ b/src/main/clojure/conexp/fca/smeasure.clj @@ -653,9 +653,7 @@ (let [C (first queue)] (let [covering-C (direct-lower-concepts ctx C) ;; those not containing g can be added since they are in cover with a concept containing c - out (println "out " covering-C) new-C (difference covering-C BV) ;; only continue with those that contain g to ensure selection criteria - for-queue (filter #(contains? (first %) g) new-C) - out (println "queue " for-queue)] + for-queue (filter #(contains? (first %) g) new-C)] (recur (into BV new-C) (into (disj queue C) for-queue)))))))) From c12a874e962bf02882f366627c8480e780f01077 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Tue, 16 May 2023 15:20:13 +0200 Subject: [PATCH 055/117] Ordinal Motifs --- AUTHORS.md | 4 +- .../clojure/conexp/fca/ordinal-motifs.clj | 504 ++++++++++++++++++ 2 files changed, 506 insertions(+), 2 deletions(-) create mode 100644 src/main/clojure/conexp/fca/ordinal-motifs.clj diff --git a/AUTHORS.md b/AUTHORS.md index 84edbb8ae..0cba6d069 100644 --- a/AUTHORS.md +++ b/AUTHORS.md @@ -11,9 +11,9 @@ Additional Contributors are * Immanuel Albrecht (Context Editor Plugin for the GUI) * Sebastian Benner (API) * Stefan Borgwardt (Shared Intents) -* Jana Fischer (json format) +* Jana Fischer (json format,Ordinal Motifs) * Tom Hanika (Concept Probability) -* Johannes Hirth (pq-cores) +* Johannes Hirth (pq-cores,Ordinal Motifs) * Gleb Kanterov (interval-scale) * Maximilian Marx (Wikidata) * Maximilian Stubbemann (concept-robustness) diff --git a/src/main/clojure/conexp/fca/ordinal-motifs.clj b/src/main/clojure/conexp/fca/ordinal-motifs.clj new file mode 100644 index 000000000..60ade6dd7 --- /dev/null +++ b/src/main/clojure/conexp/fca/ordinal-motifs.clj @@ -0,0 +1,504 @@ +(ns conexp.fca.ordinal-motifs + (:require [clojure.core.reducers :as r] + [conexp.base :refer :all] + [conexp.fca.contexts :refer :all] + [conexp.io.contexts :refer :all] + [conexp.fca.implications :refer :all] + [clojure.math.combinatorics :as comb] + [clojure.algo.generic.functor :only (fmap)] + [clojure.algo.generic.collection :as generic-col]) + +;;;;;;;; ordinal motifs + +(defmulti generate-scale (fn [scale-type & rest] scale-type)) + +(defmethod generate-scale :nominal + [_ n] + (make-context (range 1 (inc n)) + (range 1 (inc n)) + =) ) + +(defmethod generate-scale :ordinal + [_ n] + (make-context (range 1 (inc n)) + (range 1 (inc n)) + <=) ) + +(defmethod generate-scale :interordinal + [_ n] + (let [leq-scale (make-context (range 1 (inc n)) + (range 1 (inc n)) + <=) + geq-scale (make-context (range 1 (inc n)) + (range 1 (inc n)) + >=)] + (context-apposition leq-scale geq-scale)) ) + +(defmethod generate-scale :contranominal + [_ n] + (make-context (range 1 (inc n)) + (range 1 (inc n)) + not=) ) + +(defmethod generate-scale :crown + [_ n] + (make-context (range 1 (inc n)) + (range 1 (inc n)) + (fn [i j] + (or (contains? #{-1 0} (- i j )) + (>= (- i j) (dec n))) ) ) ) + +;;;;;;;; verify scale-measure using concepts +(defn isomorphic-closure-systems? + "Checks is two closure systems are equivalent with respect to object-map." + [exts1 object-map exts2] + (let [mapped-exts (->> exts1 + (pmap (fn [ext] + (->> ext (map object-map) set))) + set)] + (= mapped-exts exts2))) + +;;;;;;;; identify scale-measure using extents + +(defn- map-from-tuple + "For the two base-sets sequences returns a map from base-set to + base-set2 that maps the elements depending on their position in the + sequence." + [base-set-seq base-set2-seq] + (->> (zip base-set-seq base-set2-seq) + flatten + (apply hash-map))) + +(defn- all-bijective-maps + "Returns a lazy sequence of all bijective maps from base-set into + {1,...,n}" + [base-set] + (let [targets (->> base-set count inc (range 1))] + (pmap (partial map-from-tuple base-set) (comb/permutations targets)))) + +(defn- one-bijective-map + "Returns a bijective map from base-set into + {1,...,n} depending on the position in the sequence." + [base-set-seq] + (let [targets (->> base-set-seq count inc (range 1))] + (map-from-tuple base-set-seq targets))) + +;; identify scale-measure using extents +(defn- restrict-extents-to-base-set + "For a collection of extents restricts them to the base-set. In case + the extents are a closure system the result is the closure system on + the smaller base-set." + [exts base-set] + (->> exts + (pmap (fn [ext] + (intersection base-set ext)) ) + set)) + +(defn- identify-full-scale-measures-check-all + "Checks if exts2-set is isomorph to the sub-closure system of exts1 + given by the base-set. Checks all bijective maps for this." + [exts1 base-set exts2-set] + (let [base-set-seq (seq base-set) + exts1-restricted-to-base-set (restrict-extents-to-base-set exts1 base-set) + object-maps (all-bijective-maps base-set-seq) + equal-sized (= (count exts1-restricted-to-base-set) + (count exts2-set)) ;; for computational speed-up + ] + (and equal-sized + (some + (fn [object-map] + (isomorphic-closure-systems? exts1-restricted-to-base-set + object-map + exts2-set)) + object-maps)) )) + +(defn- identify-full-scale-measures-check-one + "Checks if exts2-set is isomorph to the sub-closure system of exts1 + given by the base-set. Checks only one bijective map for this. Used + in case all bijective maps within exts2 are automorphisms." + [exts1 base-set exts2-set] + (let [base-set-seq (seq base-set) + exts1-restricted-to-base-set (restrict-extents-to-base-set exts1 base-set) + object-map (one-bijective-map base-set-seq) + equal-sized (= (count exts1-restricted-to-base-set) + (count exts2-set)) ;; for computational speed-up + ] + (and equal-sized + (isomorphic-closure-systems? exts1-restricted-to-base-set + object-map + exts2-set)))) + + + +(defn- extent-chain? + "Checks if the extents ordered by setinclusion is a linear order." + [exts] + (let [sorted-exts (sort-by exts count) + sorted-exts-idxs (-> sorted-exts count dec range)] + (every? (fn [i] + (subset? (nth sorted-exts i) + (nth sorted-exts (inc i)))) + sorted-exts-idxs) )) + +(defn- identify-full-scale-measures-check-ordinal + "Checks if exts2-set is isomorph to the sub-closure system of exts1 + given by the base-set. Used in case exts2 is of ordinal scale." + [exts1 base-set exts2-set] + (let [base-set-seq (seq base-set) + exts1-restricted-to-base-set (restrict-extents-to-base-set exts1 base-set) + equal-sized (= (count exts1-restricted-to-base-set) + (count exts2-set)) ;; for computational speed-up + ] + (and equal-sized + (extent-chain? exts1-restricted-to-base-set)) )) + + +(defn- identify-full-scale-measures-check-interordinal + "Checks if exts2-set is isomorph to the sub-closure system of exts1 + given by the base-set. Used in case exts2 is of ordinal scale." + [exts1 base-set exts2-set] + (let [base-set-seq (seq base-set) + exts1-restricted-to-base-set (restrict-extents-to-base-set exts1 base-set) + equal-sized (= (count exts1-restricted-to-base-set) + (count exts2-set)) ;; for computational speed-up + ] + (and equal-sized + ;; TODO Jana + ) )) + + +(defn- sized-like-a-crown? + "Checks if a set of extents is sized like a crown scale." + [exts base-set crown-exts] + (let [singletons (filter (fn [ext] (= 1 (count ext))) exts) + pairs (filter (fn [ext] (= 2 (count ext))) exts)] + (and (>= (count base-set) 2) + (= (count exts) + (count crown-exts)) + (= (count singletons) + (count base-set)) + (= (count pairs) + (count base-set))) )) + +(defn- is-of-crown-scale? + "Checks if a set of extents is sized like a crown scale. Should only be used in combination with sized-like-crown?" + [exts] + (let [pairs (filter (fn [ext] (= 2 (count ext))) exts) + [cur & other] pairs + [start second] (seq cur)] + ;; checks if there is a cycle without shortcuts within pairs + (loop [cur second + remaining (set other)] + (let [next-ext (some (fn [ext] (if (contains? ext cur) + ext)) + remaining) + next (if next-ext (first (disj next-ext cur))) + next-remaining (if next-ext + (disj remaining next-ext) + remaining)] + (if next-ext + (if (and (= next start) + (empty? next-remaining)) + true + (recur next next-remaining)) + false)) ) )) + +(defn identify-full-scale-measures-check-crown + "Checks if exts2-set is isomorph to the sub-closure system of exts1 + given by the base-set. Used in case exts2 is of crown scale." + [exts1 base-set exts2-set] + (let [base-set-seq (seq base-set) + exts1-restricted-to-base-set (restrict-extents-to-base-set exts1 base-set)] + + (and (sized-like-a-crown? exts1-restricted-to-base-set base-set exts2-set) + (is-of-crown-scale? exts1-restricted-to-base-set)) )) + +(defmulti identify-full-scale-measures (fn [scale & rest] scale)) + +(defmethod identify-full-scale-measures :nominal + [_ exts1 base-set exts2-set] + (identify-full-scale-measures-check-one exts1 base-set exts2-set)) + +(defmethod identify-full-scale-measures :contranominal + [_ exts1 base-set exts2-set] + (identify-full-scale-measures-check-one exts1 base-set exts2-set)) + +(defmethod identify-full-scale-measures :ordinal + [_ exts1 base-set exts2-set] + (identify-full-scale-measures-check-ordinal exts1 base-set exts2-set)) + +(defmethod identify-full-scale-measures :interordinal + [_ exts1 base-set exts2-set] + (identify-full-scale-measures-check-interordinal exts1 base-set exts2-set)) + +(defmethod identify-full-scale-measures :crown + [_ exts1 base-set exts2-set] + (identify-full-scale-measures-check-crown exts1 base-set exts2-set)) + + +;;;;;;;;;;;;;;;;;;;;; + +;; rough pre-selection of candidates to be checked for crown scales +(defn cycles-of-g + "Returns for an object g all cycles that can be found using the + neighbors relations. Here neighbors is a map from the objects to all + other objects that have a shared attribute. Breadth first search." + [ctx neighbours start-g] + (let [obj-seq (into [start-g] (seq (disj (objects ctx) start-g))) + obj-order (fn [obj] (doall (sort-by #(.indexOf obj-seq %) obj)))] + (loop [[cycles-so-far & other :as debug] [[start-g]] + found-cycles #{} ] + (let [candidates (get neighbours (last cycles-so-far)) + candidates (let [cycles-so-far-set (set cycles-so-far)] + (set (filter (fn [g2] + (or (= g2 start-g) + (and (not (contains? cycles-so-far-set g2)) + (not (some (fn [chain-element] + (and (not (= start-g chain-element)) + (not (= (last cycles-so-far) chain-element)) + (contains? (get neighbours chain-element) + g2)) ) + cycles-so-far)))) ) + candidates ))) + new-found-cycles (if (and (contains? candidates start-g) + (<= 3 (count cycles-so-far))) + (conj found-cycles (conj cycles-so-far start-g)) + found-cycles) + candidates-seq (if (contains? candidates start-g) + (obj-order (disj candidates start-g)) + (obj-order candidates)) + next-other (map (fn [next-g] (conj cycles-so-far next-g)) + candidates-seq) + new-other (into other next-other)] + (if (empty? new-other) + new-found-cycles + (recur new-other new-found-cycles)))))) + +(defn- shares-an-attribute-relation-map + "Returns a map given by the 'shares an attribute' relation between the + objects. Diagonal is excluded." + [ctx] + (let [obj (objects ctx)] + (reduce (fn [neighbours g] + (let [attr (object-derivation ctx #{g}) + g-neighbours (set (filter (fn [g2] + (not (empty? + (intersection (object-derivation ctx #{g2}) + attr)))) + (disj obj g)))] + (assoc neighbours g g-neighbours) )) + {} + obj))) + +(defn- crown-candidates + "Returns the set of all cycles within the set of objects using the + 'shares an attribute' relation." + [ctx] + (let [obj (objects ctx) + neighbors (shares-an-attribute-relation-map ctx)] + (->> obj + (pmap (fn [g] (cycles-of-g ctx neighbors g))) ;; all cycles per object using the 'shares an attribute relation' + (reduce into) ;; all cycles in G using the 'shares an attribute relation' + (map set) set) ;; set of sets + )) + + + +(defmulti scale-complex (fn [scale-type & rest] scale-type)) + +;; TODO reduce computational time +(defn- candidates-by-subset-heredity + "Returns only those subsets of G such that all subsets are in the complex." + [complex obj subset-size] + (let [candidates (pmap set (comb/combinations (seq obj) subset-size)) + ;; only subsets of G such that each subset is already of the scale familiy + candidates (r/foldcat (r/filter + (fn [objects] + (let [subsets (map set (comb/combinations (seq objects) + (dec subset-size)))] + (every? #(contains? complex %) + subsets) )) + candidates))] + candidates)) + +(defn- objects-sets-of-scale-type + "Filters object-sets to those that are of the scale-type" + [object-sets scale-type exts scale-extents] + (->> object-sets + (r/filter (fn [object-set] + (identify-full-scale-measures scale-type + exts object-set scale-extents))) + r/foldcat)) + +(defmethod scale-complex :default + [scale-type ctx] + (let [exts (extents ctx)] + (loop [subset-size 2 + scale-complex (into #{#{}} (map (fn [g] #{g}) (objects ctx)))] + (let [candidates (candidates-by-subset-heredity scale-complex (objects ctx) subset-size) + scale-extents (-> scale-type (generate-scale subset-size) extents set)] + (if (empty? candidates) + scale-complex + (let [found-full-scale-measures (objects-sets-of-scale-type candidates scale-type exts scale-extents) + new-scale-complex (into scale-complex found-full-scale-measures)] + (recur (inc subset-size) new-scale-complex)) )) )) ) + +(defmethod scale-complex :crown + [scale-type ctx] + (let [exts (extents ctx) + candidates (crown-candidates ctx)] + (filter (fn [base-set] + (let [exts2-set (set (extents (generate-scale :crown (count base-set))))] + (identify-full-scale-measures :crown exts base-set exts2-set))) + candidates)) ) + + + +;;;;;;;; Scale complex +(defn maximal-sets [sets] + (let [comparator (fn [s1] + (fn [s2] + (and (subset? s1 s2) + (not= s1 s2)) )) + sets (pmap set sets)] + (r/foldcat (r/filter (fn [s1] (not (some (comparator s1) sets))) + sets)))) + +(defprotocol Complex + (context [this]) + (nominal-complex [this]) + (ordinal-complex [this]) + (interordinal-complex [this]) + (contranominal-complex [this]) + (crown-complex [this])) + +(defrecord Scale-Complex [ctx nominal-complex + ordinal-complex + interordinal-complex + contranominal-complex + crown-complex] + Complex + (context [this] ctx) + (nominal-complex [this] nominal-complex) + (ordinal-complex [this] ordinal-complex) + (interordinal-complex [this] interordinal-complex) + (contranominal-complex [this] contranominal-complex) + (crown-complex [this] crown-complex)) + +(defn make-scale-complex [ctx] + (let [nominal-complex (delay (scale-complex :nominal ctx)) + ordinal-complex (delay (scale-complex :ordinal ctx)) + interordinal-complex (delay (scale-complex :interordinal ctx)) + contranominal-complex (delay (scale-complex :contranominal ctx)) + crown-complex (delay (scale-complex :crown ctx))] + (->Scale-Complex ctx nominal-complex + ordinal-complex + interordinal-complex + contranominal-complex + crown-complex) )) + + + +(defmulti get-complex (fn [complex scale-type & rest] scale-type)) + +(defmethod get-complex :nominal + [s-complex _ & {:keys [maximal] :or {maximal false}}] + (let [complex (force (nominal-complex s-complex))] + (if maximal + (maximal-sets complex) + complex))) + +(defmethod get-complex :ordinal + [s-complex _ & {:keys [maximal] :or {maximal false}}] + (let [complex (force (ordinal-complex s-complex))] + (if maximal + (maximal-sets complex) + complex))) + +(defmethod get-complex :interordinal + [s-complex _ & {:keys [maximal] :or {maximal false}}] + (let [complex (force (interordinal-complex s-complex))] + (if maximal + (maximal-sets complex) + complex))) + +(defmethod get-complex :contranominal + [s-complex _ & {:keys [maximal] :or {maximal false}}] + (let [complex (force (contranominal-complex s-complex))] + (if maximal + (maximal-sets complex) + complex))) + +(defmethod get-complex :crown + [s-complex _ & {:keys [maximal] :or {maximal false}}] + (let [complex (force (crown-complex s-complex))] + (if maximal + (maximal-sets complex) + complex))) + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; + +(defprotocol Ordinal-Motif-Covering-Protocol + (ncovering [this n] [this n stats])) + +(defrecord Ordinal-Motif-Covering [covering-seq] + Ordinal-Motif-Covering-Protocol + (ncovering + [this n] + (ncovering this n false)) + (ncovering [this n stats] + (let [covering (clojure.core/take n covering-seq)] + (if stats + covering + (map first covering)))) ) + + +(defn- ordinal-motif-covering-seq + "Returns a lazy-seq of the " + ([ordinal-motifs+stats normalized] (ordinal-motif-covering-seq ordinal-motifs+stats normalized #{})) + ([ordinal-motifs+stats normalized covered-exts] + (let [;; get max key + [most-covering-motif {:keys [scale-type extents covering] :as stats}] + (apply max-key (fn [[motif {:keys [covering extents]}]] + (if normalized + (/ (count covering) (count extents)) + (count covering))) + ordinal-motifs+stats) + ;; update motif-concept-map by set difference + updated-ordinal-motifs+stats (as-> ordinal-motifs+stats $ + (dissoc $ most-covering-motif) + (fmap (fn [remaining-stats] + (update remaining-stats :covering #(difference % covering))) $ )) + new-covered-exts (clojure.set/union covered-exts covering)] + (cons [most-covering-motif stats] + (lazy-seq (ordinal-motif-covering-seq updated-ordinal-motifs+stats normalized new-covered-exts )))))) + +(defn- compute-ordinal-motifs+stats + "Computes a map for each ordinal motif base set H \\subseteq G to the extents of K[H,M]" + [scale-complex scale-types] + (let [ctx (context scale-complex)] + (reduce merge {} + (map (fn [scale-type] + (r/fold merge (r/map (fn [base-set] + (let [exts (asd-> base-set $ + (make-context $ + (attributes ctx) + (incidence ctx)) + extents + (map (partial context-object-closure ctx) $ ) + set)] + (hash-map base-set {:scale-type scale-type + :extents exts + :covering exts}))) + (get-complex scale-complex scale-type + :maximal true)))) + scale-types)) )) + +(defn greedy-motif-covering + [scale-complex & {:keys [scale-types normalized] :or {scale-types [:nominal :ordinal :interordinal :contranominal :crown] + normalized false}}] + (let [ctx (context scale-complex) + exts (extents ctx) + ordinal-motifs+stats (compute-ordinal-motifs+stats scale-complex scale-types)] + (->Ordinal-Motif-Covering + (ordinal-motif-covering-seq ordinal-motifs+stats normalized)) ) ) From e59a79cc742c8959cba8edf9db80c7bab841e533 Mon Sep 17 00:00:00 2001 From: Jana Date: Mon, 22 May 2023 11:49:03 +0200 Subject: [PATCH 056/117] reduce computational time for candidates-by-subset-heredity and identify-full-scale-measures :interordinal --- ...{ordinal-motifs.clj => ordinal_motifs.clj} | 82 +++++++++++++++---- .../conexp/fca/ordinal_motifs_test.clj | 48 +++++++++++ 2 files changed, 112 insertions(+), 18 deletions(-) rename src/main/clojure/conexp/fca/{ordinal-motifs.clj => ordinal_motifs.clj} (84%) create mode 100644 src/test/clojure/conexp/fca/ordinal_motifs_test.clj diff --git a/src/main/clojure/conexp/fca/ordinal-motifs.clj b/src/main/clojure/conexp/fca/ordinal_motifs.clj similarity index 84% rename from src/main/clojure/conexp/fca/ordinal-motifs.clj rename to src/main/clojure/conexp/fca/ordinal_motifs.clj index 60ade6dd7..294c40101 100644 --- a/src/main/clojure/conexp/fca/ordinal-motifs.clj +++ b/src/main/clojure/conexp/fca/ordinal_motifs.clj @@ -5,8 +5,8 @@ [conexp.io.contexts :refer :all] [conexp.fca.implications :refer :all] [clojure.math.combinatorics :as comb] - [clojure.algo.generic.functor :only (fmap)] - [clojure.algo.generic.collection :as generic-col]) + [clojure.algo.generic.functor :refer :all] + [clojure.algo.generic.collection :as generic-col])) ;;;;;;;; ordinal motifs @@ -152,10 +152,34 @@ (and equal-sized (extent-chain? exts1-restricted-to-base-set)) )) +(defn- get-two-element-chain + "Derives chain from extents of size 2. If no such chain exists, returns nil." + [exts-tuples] + (let [unique-elements (map first + (filter #(= (second %) 1) + (frequencies + (reduce into '() exts-tuples))))] + (if (not= (count unique-elements) 2) + nil + (loop [current-element (first unique-elements) + order [current-element] + remaining-exts (set exts-tuples) + current-exts (filter #(contains? % current-element) remaining-exts)] + (if (empty? remaining-exts) + order + (if (not= (count current-exts) 1) + nil + (let [next-element (first (difference + (first current-exts) + #{current-element})) + order (vec (concat order [next-element])) + remaining-exts (difference remaining-exts (set current-exts)) + next-exts (filter #(contains? % next-element) remaining-exts)] + (recur next-element order remaining-exts next-exts)))))))) (defn- identify-full-scale-measures-check-interordinal "Checks if exts2-set is isomorph to the sub-closure system of exts1 - given by the base-set. Used in case exts2 is of ordinal scale." + given by the base-set. Used in case exts2 is of interordinal scale." [exts1 base-set exts2-set] (let [base-set-seq (seq base-set) exts1-restricted-to-base-set (restrict-extents-to-base-set exts1 base-set) @@ -163,8 +187,25 @@ (count exts2-set)) ;; for computational speed-up ] (and equal-sized - ;; TODO Jana - ) )) + (let [exts1-two-elements (filter #(= (count %) 2) exts1-restricted-to-base-set) + exts2-two-elements (filter #(= (count %) 2) exts2-set) + equal-sized-two-elements (= (count exts1-two-elements) + (count exts2-two-elements))] + (and equal-sized-two-elements + (let [two-element-chain-exts1 (get-two-element-chain exts1-two-elements)] + (if (nil? two-element-chain-exts1) + nil + (let [two-element-chain-exts2 (get-two-element-chain exts2-two-elements) + two-element-chains-exts1 [two-element-chain-exts1 + (vec (reverse two-element-chain-exts1))] + object-maps (map #(map-from-tuple % two-element-chain-exts2) + two-element-chains-exts1)] + (some + (fn [object-map] + (isomorphic-closure-systems? exts1-restricted-to-base-set + object-map + exts2-set)) + object-maps))))))))) (defn- sized-like-a-crown? @@ -306,20 +347,25 @@ (defmulti scale-complex (fn [scale-type & rest] scale-type)) -;; TODO reduce computational time -(defn- candidates-by-subset-heredity - "Returns only those subsets of G such that all subsets are in the complex." +(defn- candidates-by-subset-heredity + "Returns only those subsets of obj such that all subsets are in the complex." [complex obj subset-size] - (let [candidates (pmap set (comb/combinations (seq obj) subset-size)) - ;; only subsets of G such that each subset is already of the scale familiy - candidates (r/foldcat (r/filter - (fn [objects] - (let [subsets (map set (comb/combinations (seq objects) - (dec subset-size)))] - (every? #(contains? complex %) - subsets) )) - candidates))] - candidates)) + (let [n-1-sized-subsets (filter #(= (count %) (dec subset-size)) complex) + n-1-sized-subsets (filter #(subset? % obj) n-1-sized-subsets) + combination-candidates (comb/combinations n-1-sized-subsets 2) + combination-candidates (filter + #(= (count (intersection (first %) (second %))) + (dec (dec subset-size))) + combination-candidates) + combinations (set (map #(union (first %) (second %)) combination-candidates)) + combinations (filter + (fn [objects] + (let [subsets (map set (comb/combinations (seq objects) + (dec subset-size)))] + (every? #(contains? complex %) + subsets) )) + combinations)] + combinations)) (defn- objects-sets-of-scale-type "Filters object-sets to those that are of the scale-type" diff --git a/src/test/clojure/conexp/fca/ordinal_motifs_test.clj b/src/test/clojure/conexp/fca/ordinal_motifs_test.clj new file mode 100644 index 000000000..f2f2fa26d --- /dev/null +++ b/src/test/clojure/conexp/fca/ordinal_motifs_test.clj @@ -0,0 +1,48 @@ +(ns conexp.fca.ordinal-motifs-test + (:use conexp.fca.ordinal-motifs) + (:use clojure.test)) + +(def exts1-list + ['(#{} #{0} #{2} #{0 2} #{1 3} #{0 1 3} #{1 2 3} #{0 1 2 3}) + '(#{} #{0} #{1} #{2} #{3} #{0 2} #{1 3} #{0 1 3} #{1 2 3} #{0 1 2} #{0 1 2 3}) + '(#{} #{0} #{1} #{2} #{3} #{0 1} #{0 2} #{0 3} #{0 1 2} #{0 1 3} #{0 1 2 3}) + '(#{} #{0} #{1} #{2} #{3} #{0 1} #{1 2} #{2 3} #{0 1 2} #{1 2 3} #{0 1 2 3}) + '(#{} #{0} #{1} #{2} #{3} #{4} #{0 1} #{1 2} #{2 3} #{3 4} #{0 1 2} #{2 3 4} #{0 1 2 3} #{0 1 2 4} #{1 2 3 4} #{0 1 2 3 4})]) + +(def exts2-list + [#{#{} #{1} #{2} #{3} #{4} #{1 2} #{2 3} #{3 4} #{1 2 3} #{2 3 4} #{1 2 3 4}} + #{#{} #{1} #{2} #{3} #{4} #{5} #{1 2} #{2 3} #{3 4} #{4 5} #{1 2 3} #{2 3 4} #{3 4 5} #{1 2 3 4} #{2 3 4 5} #{1 2 3 4 5}}]) + +(def two-element-exts1 + (mapv (fn [exts] + (filter #(= (count %) 2) exts)) + exts1-list)) + +(deftest get-two-element-chain-test + (are [two-element-exts chain] + (= (#'conexp.fca.ordinal-motifs/get-two-element-chain two-element-exts) + chain) + (get two-element-exts1 1) nil + (get two-element-exts1 2) nil + (get two-element-exts1 3) [3 2 1 0])) + +(deftest identify-full-scale-measures-check-interordinal-test + (are [exts1 base-set exts2-set result] + (= (boolean + (#'conexp.fca.ordinal-motifs/identify-full-scale-measures-check-interordinal exts1 base-set exts2-set)) + result) + (get exts1-list 0) #{0 1 2 3} (get exts2-list 0) false + (get exts1-list 1) #{0 1 2 3} (get exts2-list 0) false + (get exts1-list 2) #{0 1 2 3} (get exts2-list 0) false + (get exts1-list 3) #{0 1 2 3} (get exts2-list 0) true + (get exts1-list 4) #{0 1 2 3 4} (get exts2-list 1) false)) + +(deftest candidates-by-subset-heredity-test + (let [complex #{#{} #{0} #{1} #{2} #{3} #{4} #{0 1} #{0 2} #{0 3} #{1 2}}] + (are [complex objects subset-size result] + (= (set + (#'conexp.fca.ordinal-motifs/candidates-by-subset-heredity + complex objects subset-size))) + complex #{0 1 2 3 4} 3 #{#{0 1 2}} + complex #{0 1 2 3 4} 2 #{#{0 1} #{0 2} #{0 3} #{0 4} #{1 2} #{1 3} #{1 4} #{2 3} #{2 4} #{3 4}} + complex #{0 1 3 4} 3 #{#{}}))) From ba502d1764da9136f024f9d9bedd1756e2a5c411 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Sun, 25 Jun 2023 15:59:32 +0200 Subject: [PATCH 057/117] Added Function for Theorem 55. --- .../clojure/conexp/fca/ordinal_motifs.clj | 23 +++++++++++++++++++ 1 file changed, 23 insertions(+) diff --git a/src/main/clojure/conexp/fca/ordinal_motifs.clj b/src/main/clojure/conexp/fca/ordinal_motifs.clj index 294c40101..c8bbcb1b5 100644 --- a/src/main/clojure/conexp/fca/ordinal_motifs.clj +++ b/src/main/clojure/conexp/fca/ordinal_motifs.clj @@ -10,6 +10,29 @@ ;;;;;;;; ordinal motifs +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;FCA Theorem 55 + +(defn nominally-measurable [ctx] + (let [lat (concept-lattice ctx)] + (= (lattice-atoms lat) (lattice-sup-irreducibles lat)) +)) + +(defn ordinally-measurable [ctx] true) + +(defn interordinally-measurable [ctx]) +;TODO + +(defn contranominally-measurable [ctx] + (interordinally-measurable ctx)) + +(defn dichotomically-measurable [ctx] + (interordinally-measurable ctx)) + + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; + + (defmulti generate-scale (fn [scale-type & rest] scale-type)) (defmethod generate-scale :nominal From 7a710cb7e1c4d4c4770d268e91284c099162306d Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 28 Jun 2023 15:20:44 +0200 Subject: [PATCH 058/117] Added interordianlly-measurable Function. --- src/main/clojure/conexp/fca/ordinal_motifs.clj | 18 ++++++++++++++---- 1 file changed, 14 insertions(+), 4 deletions(-) diff --git a/src/main/clojure/conexp/fca/ordinal_motifs.clj b/src/main/clojure/conexp/fca/ordinal_motifs.clj index c8bbcb1b5..d9970b544 100644 --- a/src/main/clojure/conexp/fca/ordinal_motifs.clj +++ b/src/main/clojure/conexp/fca/ordinal_motifs.clj @@ -6,7 +6,8 @@ [conexp.fca.implications :refer :all] [clojure.math.combinatorics :as comb] [clojure.algo.generic.functor :refer :all] - [clojure.algo.generic.collection :as generic-col])) + [clojure.algo.generic.collection :as generic-col] + [clojure.set :as set])) ;;;;;;;; ordinal motifs @@ -20,8 +21,18 @@ (defn ordinally-measurable [ctx] true) -(defn interordinally-measurable [ctx]) -;TODO +(defn interordinally-measurable [ctx] + (let [objects (objects ctx) attributes (attributes ctx)] + (every? identity (concat + (for [g objects h objects] + ;does not contravene {g}' subseteq {h}' => {g}'={h}' + (or (not (subset? (object-derivation ctx #{g}) (object-derivation ctx #{h}))) + (= (object-derivation ctx #{g}) (object-derivation ctx #{h})))) + (for [m attributes] + ;does not contravene (G\{m}')''=G\{m}' + (= (attribute-derivation ctx (object-derivation ctx (set/difference objects (attribute-derivation ctx #{m})))) + (set/difference objects (attribute-derivation ctx #{m})))))) +)) (defn contranominally-measurable [ctx] (interordinally-measurable ctx)) @@ -29,7 +40,6 @@ (defn dichotomically-measurable [ctx] (interordinally-measurable ctx)) - ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; From 7c0a4b46b1291f5fc9841d9147a9f0274a5e8828 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 28 Jun 2023 18:23:18 +0200 Subject: [PATCH 059/117] Added accepts-scale Function. --- .../clojure/conexp/fca/ordinal_motifs.clj | 26 +++++++++++++++++++ 1 file changed, 26 insertions(+) diff --git a/src/main/clojure/conexp/fca/ordinal_motifs.clj b/src/main/clojure/conexp/fca/ordinal_motifs.clj index d9970b544..be27f3f05 100644 --- a/src/main/clojure/conexp/fca/ordinal_motifs.clj +++ b/src/main/clojure/conexp/fca/ordinal_motifs.clj @@ -581,3 +581,29 @@ ordinal-motifs+stats (compute-ordinal-motifs+stats scale-complex scale-types)] (->Ordinal-Motif-Covering (ordinal-motif-covering-seq ordinal-motifs+stats normalized)) ) ) + + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;tests if there is a scale-measure from a context into a standard scale of size |G| + +(defmulti accepts-scale (fn [type ctx] type)) + +(defmethod accepts-scale :nominal [type ctx] + (let [objects (objects ctx)] + (every? identity (for [g objects] + (= #{g} (attribute-derivation ctx (object-derivation ctx #{g})))))) +) + +(defmethod accepts-scale :contranominal [type ctx] + (let [objects (objects ctx)] + (valid-scale-measure? + (make-smeasure-nc ctx + (generate-scale :contranominal (count objects)) + (one-bijective-map objects))))) + +(defmethod accepts-scale :ordinal [type ctx]);exhaustive search + +(defmethod accepts-scale :interordinal [type ctx]);exhaustive search + +(defmethod accepts-scale :crown [type ctx]);exhaustive search + From 666de45f1b8e2666aa40ccc222efe91abd9986b2 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 28 Jun 2023 20:27:39 +0200 Subject: [PATCH 060/117] Implemented ordinal Variant. --- src/main/clojure/conexp/fca/ordinal_motifs.clj | 1 + 1 file changed, 1 insertion(+) diff --git a/src/main/clojure/conexp/fca/ordinal_motifs.clj b/src/main/clojure/conexp/fca/ordinal_motifs.clj index be27f3f05..9d3d26548 100644 --- a/src/main/clojure/conexp/fca/ordinal_motifs.clj +++ b/src/main/clojure/conexp/fca/ordinal_motifs.clj @@ -4,6 +4,7 @@ [conexp.fca.contexts :refer :all] [conexp.io.contexts :refer :all] [conexp.fca.implications :refer :all] + [conexp.fca.smeasure :refer :all] [clojure.math.combinatorics :as comb] [clojure.algo.generic.functor :refer :all] [clojure.algo.generic.collection :as generic-col] From 3e6a80244b66ea6afa2b3ad21a88360c1552cf02 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Tue, 8 Aug 2023 19:45:18 +0200 Subject: [PATCH 061/117] Implemented ordinal case for accepts-scale method. --- .../clojure/conexp/fca/ordinal_motifs.clj | 39 ++++++++++++++++++- 1 file changed, 38 insertions(+), 1 deletion(-) diff --git a/src/main/clojure/conexp/fca/ordinal_motifs.clj b/src/main/clojure/conexp/fca/ordinal_motifs.clj index 9d3d26548..5d6f6ba1c 100644 --- a/src/main/clojure/conexp/fca/ordinal_motifs.clj +++ b/src/main/clojure/conexp/fca/ordinal_motifs.clj @@ -3,6 +3,7 @@ [conexp.base :refer :all] [conexp.fca.contexts :refer :all] [conexp.io.contexts :refer :all] + [conexp.fca.lattices :refer :all] [conexp.fca.implications :refer :all] [conexp.fca.smeasure :refer :all] [clojure.math.combinatorics :as comb] @@ -602,9 +603,45 @@ (generate-scale :contranominal (count objects)) (one-bijective-map objects))))) -(defmethod accepts-scale :ordinal [type ctx]);exhaustive search + +(defmethod accepts-scale :ordinal [type ctx] + (let [concepts (concepts ctx) + len (count (objects ctx))] +(println concepts) + (loop [current #{} chain [] conc concepts] +(println chain) + (if ( =(count chain) len) chain + (let [new-candidates (filter #(= (count (set/difference (first %) current)) 1) conc) + next (first (first new-candidates))] + (println) + (println chain) + (println current) + (println new-candidates) + (println next) + (println conc) + (if (some? next) (recur + next + (conj chain next) + conc) + + (if (not= (count current) 0) (recur + (last (drop-last chain)) + (drop-last chain) + (filter #(not= (first %) current) conc)))) + ))) + + ) +) + (defmethod accepts-scale :interordinal [type ctx]);exhaustive search (defmethod accepts-scale :crown [type ctx]);exhaustive search + + +;test contexts + +(def ctx (make-context #{"A" "B" "C" "D"} #{1 2 3 4 5} #{["A" 1] ["B" 1] ["B" 2] ["C" 1] ["C" 2] ["C" 3] ["D" 1] ["D" 2] ["D" 3] ["D" 4] ["D" 5]})) +(def ctx2 (make-context #{"A" "B" "C" "D"} #{1 2 3 4 5} #{["A" 1] ["B" 1] ["C" 1] ["C" 2] ["C" 3] ["D" 1] ["D" 2] ["D" 3] ["D" 4] ["D" 5]})) + From caca56464a2463a939259ff3bda7c433c5c5ecd8 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 10 Aug 2023 23:00:37 +0200 Subject: [PATCH 062/117] Started implementing interordianl version for accepts-scale function. --- .../clojure/conexp/fca/ordinal_motifs.clj | 37 ++++++++++++------- 1 file changed, 24 insertions(+), 13 deletions(-) diff --git a/src/main/clojure/conexp/fca/ordinal_motifs.clj b/src/main/clojure/conexp/fca/ordinal_motifs.clj index 5d6f6ba1c..51f19b23a 100644 --- a/src/main/clojure/conexp/fca/ordinal_motifs.clj +++ b/src/main/clojure/conexp/fca/ordinal_motifs.clj @@ -607,18 +607,10 @@ (defmethod accepts-scale :ordinal [type ctx] (let [concepts (concepts ctx) len (count (objects ctx))] -(println concepts) (loop [current #{} chain [] conc concepts] -(println chain) (if ( =(count chain) len) chain (let [new-candidates (filter #(= (count (set/difference (first %) current)) 1) conc) next (first (first new-candidates))] - (println) - (println chain) - (println current) - (println new-candidates) - (println next) - (println conc) (if (some? next) (recur next (conj chain next) @@ -627,14 +619,30 @@ (if (not= (count current) 0) (recur (last (drop-last chain)) (drop-last chain) - (filter #(not= (first %) current) conc)))) - ))) - - ) + (filter #(not= (first %) current) conc)))))))) ) +;not functional +(defmethod accepts-scale :interordinal [type ctx] + (let [concepts (concepts ctx) + extents (filter first concepts) + objects (objects ctx) + len (count (objects ctx))] + (loop [current #{} chain [] conc concepts] + (if ( =(count chain) len) chain + (let [new-candidates (filter #(and (= (count (set/difference (first %) current)) 1) + (some (fn [x] (= x (set/difference objects current))) extents)) conc) + next (first (first new-candidates))] + (if (some? next) (recur + next + (conj chain next) + conc) -(defmethod accepts-scale :interordinal [type ctx]);exhaustive search + (if (not= (count current) 0) (recur + (last (drop-last chain)) + (drop-last chain) + (filter #(not= (first %) current) conc)))))))) +) (defmethod accepts-scale :crown [type ctx]);exhaustive search @@ -645,3 +653,6 @@ (def ctx (make-context #{"A" "B" "C" "D"} #{1 2 3 4 5} #{["A" 1] ["B" 1] ["B" 2] ["C" 1] ["C" 2] ["C" 3] ["D" 1] ["D" 2] ["D" 3] ["D" 4] ["D" 5]})) (def ctx2 (make-context #{"A" "B" "C" "D"} #{1 2 3 4 5} #{["A" 1] ["B" 1] ["C" 1] ["C" 2] ["C" 3] ["D" 1] ["D" 2] ["D" 3] ["D" 4] ["D" 5]})) +(def ctx3 (make-context #{"A" "B" "C" "D"} #{1 2 3 4 5 6} #{["A" 1] ["A" 2] ["A" 3] ["A" 4] ["B" 2] ["B" 3] ["B" 4] ["B" 5] + ["C" 3] ["C" 4] ["C" 5] ["C" 6] ["D" 2] ["D" 3] ["D" 4] ["D" 5]})) + From 8594e2c2691431320e59143e7b35f13305c2610f Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Fri, 11 Aug 2023 16:59:03 +0200 Subject: [PATCH 063/117] Implemented interordinal version of accepts-scale function. --- .../clojure/conexp/fca/ordinal_motifs.clj | 43 +++++++++++++------ 1 file changed, 30 insertions(+), 13 deletions(-) diff --git a/src/main/clojure/conexp/fca/ordinal_motifs.clj b/src/main/clojure/conexp/fca/ordinal_motifs.clj index 51f19b23a..430724865 100644 --- a/src/main/clojure/conexp/fca/ordinal_motifs.clj +++ b/src/main/clojure/conexp/fca/ordinal_motifs.clj @@ -609,7 +609,8 @@ len (count (objects ctx))] (loop [current #{} chain [] conc concepts] (if ( =(count chain) len) chain - (let [new-candidates (filter #(= (count (set/difference (first %) current)) 1) conc) + (let [new-candidates (filter #(and (subset? current (first %)) + ( = (count (set/difference (first %) current)) 1)) conc) next (first (first new-candidates))] (if (some? next) (recur next @@ -622,28 +623,32 @@ (filter #(not= (first %) current) conc)))))))) ) -;not functional (defmethod accepts-scale :interordinal [type ctx] (let [concepts (concepts ctx) - extents (filter first concepts) - objects (objects ctx) - len (count (objects ctx))] - (loop [current #{} chain [] conc concepts] + extents (map first concepts) + objs (objects ctx) + len (count objs)] + (loop [current #{} chain [] ext extents] + (if ( =(count chain) len) chain - (let [new-candidates (filter #(and (= (count (set/difference (first %) current)) 1) - (some (fn [x] (= x (set/difference objects current))) extents)) conc) - next (first (first new-candidates))] + (let [new-candidates (filter #(and (subset? current %) + (= (count (set/difference % current)) 1) + (some (fn [x] (= x (set/difference objs current))) ext)) ext) + next (first new-candidates)] + (println current) + (println new-candidates) (if (some? next) (recur next (conj chain next) - conc) + ext) (if (not= (count current) 0) (recur - (last (drop-last chain)) - (drop-last chain) - (filter #(not= (first %) current) conc)))))))) + (last (drop-last chain)) + (drop-last chain) + (filter #(not= % current) ext)))))))) ) + (defmethod accepts-scale :crown [type ctx]);exhaustive search @@ -656,3 +661,15 @@ (def ctx3 (make-context #{"A" "B" "C" "D"} #{1 2 3 4 5 6} #{["A" 1] ["A" 2] ["A" 3] ["A" 4] ["B" 2] ["B" 3] ["B" 4] ["B" 5] ["C" 3] ["C" 4] ["C" 5] ["C" 6] ["D" 2] ["D" 3] ["D" 4] ["D" 5]})) +(def ctx4 (make-context #{"A" "B" "C" "D" "E" "F"} #{1 2 3 12 23 123} + #{["A" 1] ["A" 12] ["A" 123] + ["B" 2] ["B" 12] ["B" 23] ["B" 123] + ["C" 3] ["C" 23] ["C" 123] + ["D" 12] ["D" 123] + ["E" 23] ["E" 123] + ["F" 123]} + )) + +(def ctx5 (make-context #{"A" "B" "C"} #{1 2 3 4 5 6} #{["A" 1] ["A" 2] ["A" 3] ["A" 4] ["B" 2] ["B" 3] ["B" 4] ["B" 5] + ["C" 3] ["C" 4] ["C" 5] ["C" 6]})) + From 9ee653a65135e9dd7ea34bc4ed2742638f98c818 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Sun, 20 Aug 2023 16:50:57 +0200 Subject: [PATCH 064/117] Preliminary Implementation for :crown Version of accepts-scale Function. --- src/main/clojure/conexp/fca/ordinal_motifs.clj | 18 ++++++++++++++++-- 1 file changed, 16 insertions(+), 2 deletions(-) diff --git a/src/main/clojure/conexp/fca/ordinal_motifs.clj b/src/main/clojure/conexp/fca/ordinal_motifs.clj index 430724865..88c067c66 100644 --- a/src/main/clojure/conexp/fca/ordinal_motifs.clj +++ b/src/main/clojure/conexp/fca/ordinal_motifs.clj @@ -649,8 +649,14 @@ ) -(defmethod accepts-scale :crown [type ctx]);exhaustive search - +(defmethod accepts-scale :crown [type ctx] + (let [objects (objects ctx) + obj-pairs (filter #(= 2 (count %)) (extents ctx)) + possible-paths (filter #(= (count objects) (count %)) (subsets obj-pairs)) + ] + (if (every? #(= #{%} (attribute-derivation ctx (object-derivation ctx #{%}))) objects);check if all objects form concepts + (some identity (for [p possible-paths] (is-of-crown-scale? p))) +))) ;test contexts @@ -673,3 +679,11 @@ (def ctx5 (make-context #{"A" "B" "C"} #{1 2 3 4 5 6} #{["A" 1] ["A" 2] ["A" 3] ["A" 4] ["B" 2] ["B" 3] ["B" 4] ["B" 5] ["C" 3] ["C" 4] ["C" 5] ["C" 6]})) +(def ctx6 (make-context #{"A" "B" "C" "D"} #{1 2 3 4} #{["A" 1] ["A" 2] ["B" 2] ["B" 3] ["C" 3] ["C" 4] ["D" 4] ["D" 1]})) + +(def ctx7 (make-context #{"A" "B" "C" "D"} #{1 2 3 4} #{["A" 1] ["A" 2] ["B" 2] ["B" 3] ["C" 3] ["C" 4] ["D" 4] ["D" 1]})) + +(def ctx8 (make-context #{"A" "B" "C" "D"} #{1 2 3 4} #{["A" 1] ["A" 2] ["A" 3] ["A" 4] + ["B" 1] ["B" 2] ["B" 3] ["B" 4] + ["C" 1] ["C" 2] ["C" 3] ["C" 4] + ["D" 1] ["D" 2] ["D" 3] ["D" 4]})) From 7ddcb3e7f0161392dfb0f0abb4b07f461f23b003 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Tue, 22 Aug 2023 22:35:35 +0200 Subject: [PATCH 065/117] Improved Implementation for crown variant of accepts-scale Function. --- .../clojure/conexp/fca/ordinal_motifs.clj | 33 +++++++++++++++---- 1 file changed, 26 insertions(+), 7 deletions(-) diff --git a/src/main/clojure/conexp/fca/ordinal_motifs.clj b/src/main/clojure/conexp/fca/ordinal_motifs.clj index 88c067c66..52bd94e97 100644 --- a/src/main/clojure/conexp/fca/ordinal_motifs.clj +++ b/src/main/clojure/conexp/fca/ordinal_motifs.clj @@ -635,8 +635,6 @@ (= (count (set/difference % current)) 1) (some (fn [x] (= x (set/difference objs current))) ext)) ext) next (first new-candidates)] - (println current) - (println new-candidates) (if (some? next) (recur next (conj chain next) @@ -651,12 +649,33 @@ (defmethod accepts-scale :crown [type ctx] (let [objects (objects ctx) - obj-pairs (filter #(= 2 (count %)) (extents ctx)) - possible-paths (filter #(= (count objects) (count %)) (subsets obj-pairs)) - ] + obj-pairs (filter #(= 2 (count %)) (extents ctx))] + (if (every? #(= #{%} (attribute-derivation ctx (object-derivation ctx #{%}))) objects);check if all objects form concepts - (some identity (for [p possible-paths] (is-of-crown-scale? p))) -))) + (loop [path [] + search-tree (into [] obj-pairs)] + + + (if (and (= ( count path) (count objects));cycle has correct length + (set/difference (second path) (set/difference (first path) (last path))));first and last elements overlap with unique element + + path + (let [candidates (filter #(= (count (set/intersection ;pair overlaps with last pair but on a new element + (set/difference + (first path) + (second path)) + %)) + 1) + (set/difference (set obj-pairs) (set path))) + + [next & updated-search-tree] (into (into [] candidates) search-tree)] + + + (if candidates (recur (into (vector next) path) updated-search-tree) + (recur (into (vector next) (drop 1 path)) updated-search-tree)) +)))))) + + ;test contexts From 563b9ae212f7a99877437410fa5aec386c37ec34 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 7 Sep 2023 19:04:35 +0200 Subject: [PATCH 066/117] Implemented Methods for Generating Distributive Lattice from three Elements and Testing if an Element is Neutral. --- src/main/clojure/conexp/fca/metrics.clj | 894 +++++++++++++++++++++++- 1 file changed, 892 insertions(+), 2 deletions(-) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 6068d1650..ef0e7e81f 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -19,7 +19,821 @@ context-object-closure object-derivation random-context objects attributes - context? concept?]] + context? concept? + diag-context + adiag-context + rand-context]];temp + [exploration :refer :all] + [fast :refer [with-binary-context + to-bitset + bitwise-context-attribute-closure + bitwise-object-derivation + bitwise-attribute-derivation concepts]] + [implications :refer :all] + [lattices :refer [inf sup lattice-base-set make-lattice make-lattice-nc + concept-lattice lattice-order extract-context-from-bv + distributive?]]] + [clojure.set :as set] + [conexp.math.util :refer [eval-polynomial binomial-coefficient]]) + (:import [conexp.fca.lattices Lattice] + [java.util ArrayList BitSet])) + + +;; help (outsource me) +(defn log2 [n] + (/ (Math/log n) (Math/log 2))) + +;;; Concept Stability and the like + +(defn concept-stability + "Compute the concept stability of `concept' in `context'." + [context concept] + + (assert (context? context) + "First argument must be a formal context.") + (assert (and (vector? concept) + (= 2 (count concept)) + (concept? context concept)) + "Second argument must be a formal concept of the given context.") + + (let [[extent intent] [(first concept) (second concept)] + counter (fn counter + ;; Perform depth-first search to count all subsets of + ;; `extent' whose derivation in context yields `intent'. + ;; For this we keep the list `fixed-included' of already + ;; considered elements to be included in the target + ;; subset of `extent', and the list `unfixed' of + ;; unconsidered elements for which it is still to be + ;; decided of whether they will be included or not. + [fixed-included unfixed] + (if (empty? unfixed) + 1 + (let [some-element (first unfixed)] + (+ (counter (conj fixed-included some-element) + (disj unfixed some-element)) + (if (= intent + (object-derivation context + (union fixed-included + (disj unfixed some-element)))) + (counter fixed-included (disj unfixed some-element)) + 0)))))] + (/ (counter #{} extent) + (expt 2 (count extent))))) + +(defn separation-index + "The concept separation is an importance measure for concepts. It + computes the size AxB (c-inc) relative to uncovered incidences Ax(M-B) + and (G-A)xB (o-inc). Max value is 1. + + Klimushkin M., Obiedkov S., Roth C. (2010) Approaches to the + Selection of Relevant Concepts in the Case of Noisy Data. In: Kwuida + L., Sertkaya B. (eds) Formal Concept Analysis. ICFCA 2010. Lecture + Notes in Computer Science, vol 5986. Springer, Berlin, + Heidelberg. https://doi.org/10.1007/978-3-642-11928-6_18" + [context concept] + (assert (context? context) + "First argument must be a formal context.") + (assert (and (vector? concept) + (= 2 (count concept)) + (concept? context concept)) + "Second argument must be a formal concept of the given context.") + (let [[extent intent] concept + c-inc (* (count extent) (count intent)) + g-inc (reduce + + (map + #(count (object-derivation context #{%})) + extent)) + a-inc (reduce + + (map #(count (attribute-derivation context #{%})) + intent)) + o-inc (- (+ g-inc a-inc) + c-inc)] ; is at least c-inc large + (/ c-inc o-inc))) + +(def ^:dynamic *fast-computation* + "Enable computation of concept probability with floating point arithmetic + instead of rationals" + nil) + +(defn concept-probability + "Compute the probability of a `concept' in `context' 𝕂 in the following manner. + Let pₘ be the relative frequence of attribute m in context. The + probability of a subset B ⊆ M in 𝕂 is the product of all pₘ for m ∈ B. + Then the probability of a concept is defined by pr(A,B) := pr(B=B'') + which is ∑_{k=0}^n {n choose k}·p_Bᵏ·(1-p_B)ⁿ⁻ᵏ·∏_{m ∈ M ∖ B}(1-p_mᵏ)." + [context concept] + (let [nr_of_objects (count (objects context)) + n (if *fast-computation* (double nr_of_objects) nr_of_objects) + M (attributes context) + B (second concept) ; intent of concept + P_M_B (mapv #(/ (count (attribute-derivation context #{%})) n ) (difference M B)) + p_B (r/fold * (map #(/ (count (attribute-derivation context #{%})) n) B)) + one_minus_p_B_n (expt (- 1 p_B) n)] + (if (not= (double p_B) 1.0) ;; if concept's extent= n + (loop [k 1 ;; since for k=0 the last term is 0, we can start with 1 + result 0 + binomial n ;; since k=0 the start binomial is n + p_B_k p_B + one_minus_p_B_k (/ one_minus_p_B_n (- 1 p_B)) + P_M_B_k P_M_B ] + (if (or (== k n) (== p_B_k 0)) ;; either done or underflowed probability (double) + result + (let [new_res + (* binomial p_B_k one_minus_p_B_k + (r/fold * (map #(- 1 %) P_M_B_k)))] + (recur + (inc k) + (+ new_res result) + (* binomial (/ (- n k) (inc k))) + (* p_B_k p_B) + (/ one_minus_p_B_k (- 1 p_B)) + (mapv (partial *) P_M_B_k P_M_B))))) + 1))) + + +;;; Robustness of Concepts + +(defn- concept-robustness-add-next-entry + "Helper-function for `concept-robustness-polynomial'. + + This function computes the value e(Y,`concept'), based on the already computed + values e(Z,`concept'), which are given in the second parameter `cache' in the + form [Z, e(Z, `concept')]. + + This function is needed in the algorithm on page 19 in \"Finding Robust + Itemsets under Subsampling\" from Tatti, Moerchen, and Calders." + [concept cache] + (let [newvalue (reduce + (fn [x V] (- x (second V))) + 0 + (filter #(subset? (second (first %)) (second concept)) + cache))] + (conj cache [concept, newvalue]))) + +(defn concept-robustness-polynomial + "Return the coefficients of the robustness polynomial of `concept'. + + For the given `concept' of a context, the coefficients of the polynomial p + corresponding to the robustness is computed by using the seq `concepts' of + all concepts of the context. The optional boolean parameter `sorted?' allows + to declare the seq of concepts as being already sorted by increasing + attribute-set. Thus if v is the result of (robustness-polynomial concept + concepts), then (eval-polynomial v (- 1 alpha)) computes the robustness with + parameter alpha. + + For details see \"Finding Robust Itemsets under Subsampling\" from Tatti, + Moerchen, and Calders, pages 17–19." + ([concept concepts sorted?] + (let [B (second concept) + used-concepts (drop 1 (if sorted? + (filter #(subset? B (second %)) concepts) + (sort-by #(count (second %)) + (filter #(subset? B (second %)) + concepts)))) + ;; store for all subconcepts (C_A,C_B) of concept the vector [C, e(C_B, concept)] + concepts-with-values (reduce + (fn [x y] + (concept-robustness-add-next-entry y x)) + [[concept, 1]] + used-concepts) + sup (count (first concept))] + ;; use the above computed values [C, e(C_B, concept)] to compute the polynomial + (reduce + (fn [old-coefficients entry] + (let [index (- sup (count (first (first entry))))] + (assoc old-coefficients + index (+ (nth old-coefficients index) (second entry))))) + (vec (take (+ 1 sup) (repeat 0))) + concepts-with-values))) + ([concept concepts] + (concept-robustness-polynomial concept concepts false))) + +(defn concept-robustness + "Computes the robustness of a `concept' in a context with parameter `alpha' by + using the seq `concepts' consisting of all concepts of the context. The + optional boolean parameter `sorted?' allows to declare the seq of concepts as + beeing already sorted by increasing size of the attribute set. This function + uses the function concept-robustness-polynomial." + ([concept concepts alpha sorted?] + (assert (and (number? alpha) + (<= 0 alpha 1)) + "Third argument must be between 0 and 1!") + (eval-polynomial (concept-robustness-polynomial concept concepts sorted?) (- 1 alpha))) + ([concept concepts alpha] + (concept-robustness concept concepts alpha false))) + +(defn average-concept-robustness + "Takes the seq `concepts' consisting of all concepts of a context and computes + the average concept robustness with parmater `alpha'." + [concepts alpha] + (assert (and (number? alpha) + (<= 0 alpha 1)) + "Second argument must be between 0 and 1!") + (let [sorted-concepts (sort-by + #(count (second %)) + concepts) + n (count sorted-concepts) + robustness-values (map + #(concept-robustness + (nth sorted-concepts %) + (drop % sorted-concepts) + alpha + true) + (range 0 n))] + (/ (reduce + robustness-values) n))) + + +;;; Similarity Measures for Concepts (implemented by Anselm von Wangenheim) + +(defn jaccard-index + "Computes the Jaccard index of two sets. This is |x ∩ y| / |x ∪ y|. + Returns 1 if both sets are empty." + [x y] + (if (and (empty? x) (empty? y)) + 1 + (/ (count (intersection x y)) (count (union x y))))) + +(defn sorensen-coefficient + "Computes the Sorensen coefficient of two sets. + This is 2 * |x ∩ y| / (|x| + |y|). + Returns 1 if both sets are empty." + [x y] + (if (and (empty? x) (empty? y)) + 1 + (/ (* 2 (count (intersection x y))) (+ (count x) (count y))))) + +(defn weighted-concept-similarity + "Computes a weighted concept similarity for a given similatity measure `sim', + two concepts [`c1' `c2'] and an optional weight `w' (default is 1/2). + + That is the weighted average of the similarity of the extents/object sets + (weight `w') and the intents/attribute sets (weight 1-`w'). + + This is from Alqadah, F. & Bhatnagar, R. (2011), 'Similarity measures in + formal concept analysis.', Ann. Math. Artif. Intell. 61 (3), 249, + https://doi.org/10.1007/s10472-011-9257-7" + ([sim [c1 c2]] (weighted-concept-similarity sim [c1 c2] (/ 1 2))) + ([sim [c1 c2] w] + (assert (and (number? w) + (<= 0 w 1)) + "Thrid argument must be between 0 and 1!") + (+ + (* w (sim (c1 0) (c2 0))) + (* (- 1 w) (sim (c1 1) (c2 1)))))) + + + +;;; Concept stability + +(defn mcs-stability-approximation + "Approximates concept stability with Markov Chains." + [ctx concept sample-size] + (let [counter (atom 0)] + (doall + (for [i (range sample-size)] + (let [prem (first concept) + concl (second concept) + limit (count concl)] + (if (= (attribute-derivation ctx + (take (rand-int limit) + (shuffle concl))) + prem) + (swap! counter inc))))) + (/ @counter sample-size))) + +(defn lds-stability-approximation + "Approximates concept stability with Low-Discrepancy Sampling. The function + takes a context and concept, the sample-size and base (both as integer). + An additional argument may be given to choose the sampling method. + The options are: + :sobol One-dimensional Sobol Sequence (default) + :svdc Scrambled Van der Corput Sequence + + Function based on 'An Efficient Approximation of Concept + Stability Using Low-Discrepancy Sampling' Ibrahim; Missaoui 2018 + https://link.springer.com/chapter/10.1007/978-3-319-91379-7_3 " + ([ctx concept sample-size base] + (lds-stability-approximation ctx concept sample-size base :sobol)) + ([ctx concept sample-size base sampling-method] + (let [lds (atom []) + counter (atom 0) + intent (second concept) + intent-size (count intent) + powerset (subsets intent)] + (doall + (for [i (range sample-size)] + (swap! lds conj (case sampling-method + :sobol (generate-sobol i) + :svdc (generate-svdc i base) + (generate-sobol i))))) + (doall + (for [element @lds] + (let [position (int (+ (* intent-size element) 0.5)) + subset (nth powerset position)] + (if (= (first concept) + (attribute-derivation ctx subset)) + (swap! counter inc))))) + (/ @counter sample-size)))) + +;;; standard lattice properties to some degree + +(defn satisfying-triples + "Given lattice lat, compute triples (a,b,c)∈L³ (pairwise different) + such that they fullfil a given condition. The triples may be + filtered beforehand using prefilter." + ([^Lattice lat condition] + (let [base (into [] (lattice-base-set lat))] + ;; (filter condition (filter prefilter (permuted-combinations base 3))))) + (filter condition (permuted-combinations base 3)))) + ([lat condition prefilter] + (let [base (into [] (lattice-base-set lat))] + (filter condition (filter prefilter (permuted-combinations base 3)))))) + + +(defn distributive-triples + "Given lattice lat, compute triples (x,y,z)∈L³ (pairwise different) + such that they fullfil the distributive property + x∨(y∧z)=(x∨y)∧(x∨z)." + ([^Lattice lat] + (distributive-triples lat (fn [x] true))) + ([^Lattice lat prefilter] + (let [inf (inf lat), + sup (sup lat)] + (satisfying-triples lat (fn [[x y z]] + (= (sup x (inf y z )) + (inf (sup x y) (sup x z)))) + prefilter)))) + +(defn modular-triples + "Given lattice lat, compute triples (x,y,z)∈L³ (pairwire different) + such that they fullfil the modular property x ≤ z ⇒ + x∨(y∧z)=(x∨y)∧z." + ([lat] + (modular-triples lat (fn [x] true))) + ([lat prefilter] + (let [inf (inf lat), + sup (sup lat), + ord (lattice-order lat) + base (into [] (lattice-base-set lat))] + (satisfying-triples lat (fn [[x y z]] + (if (ord x z) ;; if x≤y + (= ;; check x∨(y∧z)=(x∨y)∧z + (sup x (inf y z)) + (inf (sup x y) z)) + true)) + prefilter)))) ;; else always true + +(defn distributivity-degree + "Computes the number of triples (a,b,c)∈L³ (pairwise different) + that fullfil the distributivity law and divides it by the number of + possible pw different triples." + [lat] + (let [n (count (lattice-base-set lat))] + (if (< n 3) + 1 ;; in case we have less than 3 elements we have distributivity + (/ (count (distributive-triples lat)) + (* 6 (binomial-coefficient n 3)))))) + +(defn modularity-degree + "Computes the number of triples (a,b,c)∈L³ (pairwise different) + that fullfil the modularity law and divides it by the number of + possible pw different triples. (tbc later on)" + [lat] + (let [n (count (lattice-base-set lat))] + (if (< n 3) + 1 ;; in case we have less than 3 elements we have modularity + (/ (count (modular-triples lat)) + (* 6 (binomial-coefficient n 3)))))) + +(defn elements-distributivity + "Computes the number of triples (a,b,c)∈L³ (pw different) where either + a=e, b=e, or c=e, that fullfil the modularity law. This number is + then divided it by the number of possible pw different triples of such kind." + [lat e] + (assert (contains? (lattice-base-set lat) e)) + (let [n (count (lattice-base-set lat)), + filterfunc (fn [[x y z]] (or (= x e) (= y e) (= z e)))] + (/ (count (distributive-triples + lat filterfunc)) + (* 6 (binomial-coefficient (- n 1) 2))))) + +(defn elements-modularity + [lat e] + (assert (contains? (lattice-base-set lat) e)) + (let [n (count (lattice-base-set lat))] + (/ (count (modular-triples lat (fn [[x y z]] (or (= x e) (= y e) (= z e))))) + (* 6 (binomial-coefficient (- n 1) 2))))) + +;;; Relevant Attributes (Objects) et Al + +(defn attribute-information-entropy + "Computes the attribute-information-entropy for a given context 𝕂using the formula + (∑_{m ∈ M} 1-{m}''/|M|)/|M|, see https://doi.org/10.1007/978-3-030-23182-8_8" + [ctx] + (let [M (attributes ctx) + nr_of_attributes (count M)] + (/ (- nr_of_attributes + (r/fold + (pmap + (fn [m] (/ (count (context-attribute-closure ctx #{m})) + nr_of_attributes)) + M))) + nr_of_attributes))) + +(defn object-information-entropy + "Computes the object-information-entropy for a given context 𝕂using the formula + (∑_{g ∈ G} 1-{g}''/|G|)/|G|, see https://doi.org/10.1007/978-3-030-23182-8_8" + [ctx] + (attribute-information-entropy (dual-context ctx))) + +(defn information-entropy + "Computes the mean entropy of context ctx based on the equal + weighted sum of attribute-information-entropy and + object-information-entropy." + [ctx] + (/ (+ (attribute-information-entropy ctx) (object-information-entropy ctx)) 2)) + + +(defn shannon-attribute-information-entropy + "Computes the Shannon-attribute-information-entropy for a given context 𝕂using the formula + ∑_{m ∈ M} -{m}''/|M|· log₂ ({m}''/|M|), see https://doi.org/10.1007/978-3-030-23182-8_8" + [ctx] + (let [M (attributes ctx) + nr_of_attributes (count M)] + (r/fold + (pmap (fn [x] (- (* x (log2 x)))) + (pmap + (fn [m] (/ (count (context-attribute-closure ctx #{m})) + nr_of_attributes)) + M))))) + +(defn shannon-object-information-entropy + "Computes the Shannon-object-information-entropy for a given context 𝕂using the formula + ∑_{g ∈ G} -{g}''/|G|· log₂ ({g}''/|G|), see https://doi.org/10.1007/978-3-030-23182-8_8" + [ctx] + (shannon-attribute-information-entropy (dual-context ctx))) + +(defn shannon-attribute-information-entropy-fast + "Computes the Shannon-attribute-information-entropy for a given + context 𝕂using the formula ∑_{m ∈ M} -{m}''/|M|· log₂ ({m}''/|M|), + see https://doi.org/10.1007/978-3-030-23182-8_8. This implementation + resorts to bit vectors in order to increase the computation + speed. This conversion is not adviced for small data sets. " + [ctx] + (with-binary-context ctx + (let [a-closure-counts + (pmap (fn [y] + (let [^BitSet bs (BitSet.)] + (.set bs y) + (bitwise-context-attribute-closure + incidence-matrix + object-count + attribute-count + bs))) + (range attribute-count))] + (- + (r/fold + (map (fn [x] (* (/ (.cardinality ^BitSet x) ^long attribute-count) + (log2 (/ (.cardinality ^BitSet x) ^long attribute-count)))) + a-closure-counts)))))) + + +(defn shannon-object-information-entropy-fast + "Computes the Shannon-object-information-entropy for a given context 𝕂using the formula + ∑_{g ∈ G} -{g}''/|G|· log₂ ({g}''/|G|), see https://doi.org/10.1007/978-3-030-23182-8_8" + [ctx] + (shannon-attribute-information-entropy-fast (dual-context ctx))) + +(defn shannon-information-entropy + "Computes the mean shannon-entropy of context ctx based on the equal + weighted sum of attribute-information-entropy and + object-information-entropy." + [ctx] + (/ (+ (shannon-attribute-information-entropy ctx) + (shannon-object-information-entropy ctx)) 2)) + +(defn shannon-information-entropy-fast + "Computes the mean shannon-entropy of context ctx based on the equal + weighted sum of attribute-information-entropy and + object-information-entropy." + [ctx] + (/ (+ (shannon-attribute-information-entropy-fast ctx) + (shannon-object-information-entropy-fast ctx)) 2)) + +(defn extent-label-function + "Computes the label for given g ∈ G, i.e., the natural number n such + that n=|{c ∈ 𝔅(𝕂) ∣ g ∈ ext(c)}|, see + https://doi.org/10.1007/978-3-030-23182-8_8" + ([ctx g] + (extent-label-function ctx (concepts :in-close ctx) g)) + ([ctx concepts g] + (count + (filter (fn [x] (contains? (first x) g)) + concepts)))) + +(defn intent-label-function + "Computes the label for given m ∈ M, i.e., the natural number n such + that n=|{c ∈ 𝔅(𝕂) ∣ m ∈ int(c)}|, see + https://doi.org/10.1007/978-3-030-23182-8_8" + ([ctx m] + (extent-label-function ctx (concepts :in-close ctx) m)) + ([ctx concepts m] + (count + (filter (fn [x] (contains? (second x) m)) + concepts)))) + +(defn attribute-removal-robust-concepts + "Computes the set of concepts {c ∈ 𝔅(𝕂) ∣ (int(c) ∖ A)' = ext(c)} + for some attribute set A ⊆ M." + ([ctx A] + (attribute-removal-robust-concepts ctx (concepts :in-close ctx) A)) + ([ctx theconcepts A] + (into [] (r/filter (fn [x] (= + (attribute-derivation ctx (difference (second x) A)) + (first x))) + theconcepts)))) + +(defn object-removal-robust-concepts + "Computes the set of concepts {c ∈ 𝔅(𝕂) ∣ (ext(c) ∖ A)' = int(c)} + for some attribute set A ⊆ G." + ([ctx A] + (object-removal-robust-concepts ctx (concepts :in-close ctx) A)) + ([ctx theconcepts A] + (into [] (r/filter (fn [x] (= + (object-derivation ctx (difference (first x) A)) + (second x))) + theconcepts)))) + + +(defn relative-relevance + "Computes for formal context (G,M,I) the relative relevance of + attribute set A ⊆ M, using the formula from Proposition 3.5 in + https://doi.org/10.1007/978-3-030-23182-8_8, i.e., + r(A)=1-∑_{c∈𝔅(𝕂_A)}|ext(c)|/∑_{c∈𝔅(𝕂)}|ext(c)|, + where 𝔅(𝕂_A)={c∈𝔅(𝕂)∣(int(c)∖A)'=ext(c)}" + ([ctx A] + (relative-relevance ctx (concepts :in-close) A)) + ([ctx theconcepts A] + (let [extsum (r/fold + (map (fn [x] (count (first x))) theconcepts))] + (- 1 + (->> theconcepts + (filter + (fn [x] (= (count + (attribute-derivation ctx (difference (second x) A))) + (count (first x))))) + (pmap (fn [x] (count (first x)))) + (r/fold +) + (* (/ 1 extsum))) + )))) + +(defn relative-relevance-fast + "Compute relative-relevance using bitsets" + [ctx theconcepts A] + (with-binary-context ctx + (let [o-prime (partial bitwise-object-derivation incidence-matrix object-count attribute-count) + a-prime (partial bitwise-attribute-derivation incidence-matrix object-count attribute-count) + theextents (pmap (fn [x] (to-bitset object-vector (first x))) theconcepts) + theatts (to-bitset attribute-vector A)] + (- 1 + (/ + (r/fold + (map (fn [x] + (if (= + (let [thing (o-prime x)] + (.andNot thing theatts) ;; remove attribute set + (.cardinality (a-prime thing))) + (.cardinality x)) + (.cardinality x) + 0)) + theextents)) + (r/fold + (map (fn [x] (.cardinality x)) theextents))))))) + +(defn next-maximal-relevant + "Given a formal context (G,M,I), an attribute set A ⊆ M, this + functions computes the most relevant m ∈ M ∖ A with respect to relative-relevance." + ([ctx theconcepts] (next-maximal-relevant ctx theconcepts #{})) + ([ctx theconcepts A] + (let [atts (attributes ctx) + available-atts (difference atts A) + obs (objects ctx)] + (apply max-key (fn [x] (relative-relevance-fast ctx theconcepts (union A #{x}))) + available-atts)))) + +(defn next-n-maximal-relevant + "Based on next-maximal-relevant, compute the the next n maximal + relevant features in a consekutive manner. Please be advised, this + is not necessiraly equivalent to compute the subset N ⊆ M with |N|=n + being the most relevant wrt relative-relevance." + ([ctx theconcepts n] + (next-n-maximal-relevant ctx theconcepts n #{})) + ([ctx theconcepts n A] + (loop [[counter resultset] [0 []]] + (if (< counter n) + (recur [(inc counter) + (conj resultset + (next-maximal-relevant ctx theconcepts (set (union resultset A))))]) + resultset)))) + +(defn n-maximal-relevant + "Based on relative-relevance, compute the the subset N ⊆ M with |N|=n, + such that there is no L ⊆ M with r(N) k n) + result + (recur + (inc k) + (conj result + (let [atts (attributes ctx) + available-atts (difference atts (union A result)) + obs (objects ctx)] + (apply max-key (fn [x] + (let [pctx (make-context obs (union #{x} result A) (incidence ctx))] + (* + (count (concepts :in-close pctx)) + (object-information-entropy pctx)))) + available-atts))))))) + +(defmethod next-n-maximal-relevant-approx :shannon + ([_ ctx n] + (next-n-maximal-relevant-approx :shannon ctx n #{})) + ([_ ctx n A] + (loop [k 1 + result []] + (if (> k n) + result + (recur + (inc k) + (conj result (let [atts (attributes ctx) + available-atts (difference atts (union A result)) + obs (objects ctx)] + (apply max-key (fn [x] + (let [pctx (make-context obs (union #{x} A result) (incidence ctx))] + (* + (count (concepts :in-close pctx)) + (shannon-object-information-entropy-fast pctx)))) + available-atts)))))))) + + +(defn nRandomAtts + [ctx n] + (let [atts (attributes ctx)] + (take n (shuffle atts)))) + +;; (defn rel-consistency ??? +;; "Computes the relative consistency of a subset $N ⊆ M$ with respect to +;; a given formal context (G,M,I), and some attribute subset N ⊆ M" +;; [ctx N] +;; (let [G (objects ctx) +;; M (attributes ctx) +;; MN (difference M N) +;; ctx-N (make-context G N (incidence ctx)) +;; ctx-MN (make-context G MN (incidence ctx))] +;; (let [derive-N (fn [x] (context-object-closure ctx-N x)) +;; derive-MN (fn [x] (context-object-closure ctx-MN x))] +;; (/ +;; (count (filter (fn [x] (subset? (derive-N #{x}) (derive-MN #{x}))) G)) +;; (count G) +;; )))) + +;; ) + + +(defn generate-from-triple [triple lat] + + (let [stage1-meets (for [a triple b triple] (inf lat a b)) + stage1-joins (for [a triple b triple] (sup lat a b)) + + stage2-meets (for [a stage1-joins b stage1-joins] (inf lat a b)) + stage2-joins (for [a stage1-meets b stage1-meets] (sup lat a b)) + + final-meet (inf lat stage1-joins) + + ground-set (set/union stage1-meets + stage1-joins + stage2-meets + stage2-joins + final-meet) + order-function ;tbt + ] +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.metrics + (:require [clojure.core.reducers :as r] + [clojure.math.combinatorics :refer [permuted-combinations combinations]] + ;; [clojure.math.numeric-tower :refer [log]] + [conexp.base :refer :all] + [conexp.math.markov :refer :all] + [conexp.fca + [contexts :refer [make-context incidence dual-context + attribute-derivation + context-attribute-closure + context-object-closure + object-derivation random-context + objects attributes + context? concept? + adiag-context + rand-context]];temp [exploration :refer :all] [fast :refer [with-binary-context to-bitset @@ -786,11 +1600,87 @@ ;; ) +;returns destributive lattice generated by the concepts in "triple" +;tripe must be a collection of three concepts in "lat" +(defn generate-from-triple [triple lat] + + (let [stage1-meets (for [a triple b triple] ((inf lat) a b)) + stage1-joins (for [a triple b triple] ((sup lat) a b)) + + stage2-meets (for [a stage1-joins b stage1-joins] ((inf lat) a b)) + stage2-joins (for [a stage1-meets b stage1-meets] ((sup lat) a b)) + + final-meet ((inf lat) ((inf lat) (first stage1-joins) (second stage1-joins)) (last stage1-joins)) + + base-set (set/union stage1-meets + stage1-joins + stage2-meets + stage2-joins + final-meet) + ] + + (make-lattice-nc base-set + (lattice-order lat) + (inf lat) + (sup lat))) +) + +;verifies if "concept" is a neutral element in "lat" +(defn neutral? [concept lat] + (let [base-set (lattice-base-set lat)] + (some identity (for [x base-set y base-set] (distributive? (generate-from-triple [concept x y] lat)))) +)) + +;return all neutral elements in "lat" +(defn neutral-concepts [lat] + (let [base-set (lattice-base-set lat)] + (filter #(neutral? % lat) base-set) +) +) + +;retruns a complement of "concept" in "lat" +(defn complemnt [concept lat] + (let [base-set (lattice-base-set lat) + top ]) + + +) + +;meets: +x-y +x-z +y-z +x-y-z + +x+y-x+z +x+y-y+z +x+z-y+z + +;joins: +x+y +x+z +y+z +x+y+z + +x-y+x-z +x-y+y-z +x-z+y-z + +x-y+x-z+y-z + +;test +(def ctx (make-context #{1 2 3 4 5} + #{"A" "B" "C" "D" "E"} + #{[1 "A"] [2 "A"] [2 "B"] [3 "B"] [3 "C"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) +(def lat (concept-lattice ctx)) +((inf lat2) [#{1} 0] [#{2} 0]) + +(def lat2 (generate-from-triple [[#{5} #{"E" "C" "D"}] [#{4 3} #{"C" "B"}] [#{4 2} #{"B" "A"}]] lat)) ;;; -nil + nil From 37a7af721815f64b7803592fa44577321f2be43a Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Fri, 8 Sep 2023 21:10:22 +0200 Subject: [PATCH 067/117] Added Functions for Libkin Decomposition. --- src/main/clojure/conexp/fca/metrics.clj | 79 +++++++++++++++++-------- 1 file changed, 55 insertions(+), 24 deletions(-) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index ef0e7e81f..8ba65e1e0 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -1604,32 +1604,37 @@ ;tripe must be a collection of three concepts in "lat" (defn generate-from-triple [triple lat] - (let [stage1-meets (for [a triple b triple] ((inf lat) a b)) - stage1-joins (for [a triple b triple] ((sup lat) a b)) + (let [stage1-meets (set (filter some? (for [a triple b triple] (if (not= a b) ((inf lat) a b))))) + stage1-joins (set (filter some? (for [a triple b triple] (if (not= a b) ((sup lat) a b))))) - stage2-meets (for [a stage1-joins b stage1-joins] ((inf lat) a b)) - stage2-joins (for [a stage1-meets b stage1-meets] ((sup lat) a b)) - - final-meet ((inf lat) ((inf lat) (first stage1-joins) (second stage1-joins)) (last stage1-joins)) - - base-set (set/union stage1-meets - stage1-joins - stage2-meets - stage2-joins - final-meet) - ] - - (make-lattice-nc base-set + stage2-meets (set (filter some? (for [a stage1-joins b stage1-joins] (if (not= a b) ((inf lat) a b))))) + stage2-joins (set (filter some? (for [a stage1-meets b stage1-meets] (if (not= a b) ((sup lat) a b))))) + + + final-meet #{ (into [] ((inf lat) + ((inf lat) (first stage1-joins) (second stage1-joins)) + (last stage1-joins)))} + + base-set (set/union triple + stage1-meets + stage1-joins + stage2-meets + stage2-joins + final-meet)] + + (make-lattice-nc base-set (lattice-order lat) (inf lat) - (sup lat))) -) + (sup lat)) + +)) ;verifies if "concept" is a neutral element in "lat" (defn neutral? [concept lat] (let [base-set (lattice-base-set lat)] - (some identity (for [x base-set y base-set] (distributive? (generate-from-triple [concept x y] lat)))) -)) + (every? identity (for [x base-set y base-set] (distributive? (generate-from-triple [concept x y] lat)))) +) +) ;return all neutral elements in "lat" (defn neutral-concepts [lat] @@ -1638,14 +1643,36 @@ ) ) -;retruns a complement of "concept" in "lat" -(defn complemnt [concept lat] +;retruns all complement of "concept" in "lat" +(defn element-complement [concept lat] (let [base-set (lattice-base-set lat) - top ]) + top (first(filter #(= (second %) #{}) base-set)) + bot (reduce #(if (> (count (second %1)) (count (second %2))) %1 + %2 + ) base-set)] + + (filter #(and (not= % concept) + (= ((sup lat) concept %) top) + (= ((inf lat) concept %) bot)) + base-set)) +) + +;returns a decomposition pair of "lat", if a Libkin decomposition is possible +(defn decomposition [lat] + (let [neutral-element (first (neutral-concepts lat)) + complement (first (element-complement neutral-element lat))] + + [neutral-element complement] +) ) + + + + + ;meets: x-y x-z @@ -1673,10 +1700,14 @@ x-y+x-z+y-z #{"A" "B" "C" "D" "E"} #{[1 "A"] [2 "A"] [2 "B"] [3 "B"] [3 "C"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) (def lat (concept-lattice ctx)) -((inf lat2) [#{1} 0] [#{2} 0]) -(def lat2 (generate-from-triple [[#{5} #{"E" "C" "D"}] [#{4 3} #{"C" "B"}] [#{4 2} #{"B" "A"}]] lat)) +(def ctx2 (make-context #{1 2 3 4 5} + #{"A" "B" "C" "D" "E"} + #{[1 "A"] [2 "A"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) +(def lat2 (concept-lattice ctx)) + + From ea290b4f20565d59946cb5acc70c794c54f668ba Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 13 Sep 2023 02:26:46 +0200 Subject: [PATCH 068/117] Fully Implemented Libkin Decomposition. --- src/main/clojure/conexp/fca/metrics.clj | 20 +++++++++----------- 1 file changed, 9 insertions(+), 11 deletions(-) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 8ba65e1e0..55b004b59 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -1657,16 +1657,11 @@ base-set)) ) -;returns a decomposition pair of "lat", if a Libkin decomposition is possible -(defn decomposition [lat] - (let [neutral-element (first (neutral-concepts lat)) - complement (first (element-complement neutral-element lat))] - - [neutral-element complement] -) - - -) +;returns all decompositions pair of "lat" for Libkin decompositions +(defn decompositions [lat] + (let [neutral-elements (neutral-concepts lat)] + (for [n neutral-elements c (element-complement n lat)] [n c]) +)) @@ -1708,7 +1703,10 @@ x-y+x-z+y-z (def lat2 (concept-lattice ctx)) - +(def ctx3 (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] + [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] + [7 "A"] [7 "B"] [7 "C"]})) +(def lat3 (concept-lattice ctx3)) From b148648f352324b3a80d24708eb16180405a32e1 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 20 Sep 2023 21:07:57 +0200 Subject: [PATCH 069/117] Outsourced Functions. Implemented full Lattice Decomposition. --- .../clojure/conexp/fca/decompositions.clj | 56 ++ src/main/clojure/conexp/fca/metrics.clj | 882 +----------------- 2 files changed, 69 insertions(+), 869 deletions(-) create mode 100644 src/main/clojure/conexp/fca/decompositions.clj diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj new file mode 100644 index 000000000..df76dc144 --- /dev/null +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -0,0 +1,56 @@ +(ns conexp.fca.decompositions + (:require [conexp.base :refer :all] + [conexp.fca + [contexts :refer :all] + [metrics :refer :all] + [lattices :refer :all] + [posets :refer :all]] + )) + + +;returns all decompositions pair of "lat" for Libkin decompositions +(defn libkin-decomposition-pairs [lat] + (let [neutral-elements (neutral-concepts lat)] + (for [n neutral-elements c (element-complement n lat)] [n c]) +)) + + +(defn lattice-ideal [lat concept] + (let [base-set (lattice-base-set lat) + order (lattice-order lat) + new-base-set (filter #(order % concept) base-set)] + + (make-lattice-nc new-base-set + order + (inf lat) + (sup lat)) + +) +) + + +(defn libkin-decomposition-lattices [lat decomp-pair] + [(lattice-ideal lat (first decomp-pair)) + (lattice-ideal lat (last decomp-pair))] +) + + + + +;test +(def ctx (make-context #{1 2 3 4 5} + #{"A" "B" "C" "D" "E"} + #{[1 "A"] [2 "A"] [2 "B"] [3 "B"] [3 "C"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) +(def lat (concept-lattice ctx)) + + +(def ctx2 (make-context #{1 2 3 4 5} + #{"A" "B" "C" "D" "E"} + #{[1 "A"] [2 "A"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) +(def lat2 (concept-lattice ctx)) + + +(def ctx3 (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] + [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] + [7 "A"] [7 "B"] [7 "C"]})) +(def lat3 (concept-lattice ctx3)) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 55b004b59..48de93a31 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -9,6 +9,7 @@ (ns conexp.fca.metrics (:require [clojure.core.reducers :as r] [clojure.math.combinatorics :refer [permuted-combinations combinations]] + [clojure.set :as set] ;; [clojure.math.numeric-tower :refer [log]] [conexp.base :refer :all] [conexp.math.markov :refer :all] @@ -19,821 +20,7 @@ context-object-closure object-derivation random-context objects attributes - context? concept? - diag-context - adiag-context - rand-context]];temp - [exploration :refer :all] - [fast :refer [with-binary-context - to-bitset - bitwise-context-attribute-closure - bitwise-object-derivation - bitwise-attribute-derivation concepts]] - [implications :refer :all] - [lattices :refer [inf sup lattice-base-set make-lattice make-lattice-nc - concept-lattice lattice-order extract-context-from-bv - distributive?]]] - [clojure.set :as set] - [conexp.math.util :refer [eval-polynomial binomial-coefficient]]) - (:import [conexp.fca.lattices Lattice] - [java.util ArrayList BitSet])) - - -;; help (outsource me) -(defn log2 [n] - (/ (Math/log n) (Math/log 2))) - -;;; Concept Stability and the like - -(defn concept-stability - "Compute the concept stability of `concept' in `context'." - [context concept] - - (assert (context? context) - "First argument must be a formal context.") - (assert (and (vector? concept) - (= 2 (count concept)) - (concept? context concept)) - "Second argument must be a formal concept of the given context.") - - (let [[extent intent] [(first concept) (second concept)] - counter (fn counter - ;; Perform depth-first search to count all subsets of - ;; `extent' whose derivation in context yields `intent'. - ;; For this we keep the list `fixed-included' of already - ;; considered elements to be included in the target - ;; subset of `extent', and the list `unfixed' of - ;; unconsidered elements for which it is still to be - ;; decided of whether they will be included or not. - [fixed-included unfixed] - (if (empty? unfixed) - 1 - (let [some-element (first unfixed)] - (+ (counter (conj fixed-included some-element) - (disj unfixed some-element)) - (if (= intent - (object-derivation context - (union fixed-included - (disj unfixed some-element)))) - (counter fixed-included (disj unfixed some-element)) - 0)))))] - (/ (counter #{} extent) - (expt 2 (count extent))))) - -(defn separation-index - "The concept separation is an importance measure for concepts. It - computes the size AxB (c-inc) relative to uncovered incidences Ax(M-B) - and (G-A)xB (o-inc). Max value is 1. - - Klimushkin M., Obiedkov S., Roth C. (2010) Approaches to the - Selection of Relevant Concepts in the Case of Noisy Data. In: Kwuida - L., Sertkaya B. (eds) Formal Concept Analysis. ICFCA 2010. Lecture - Notes in Computer Science, vol 5986. Springer, Berlin, - Heidelberg. https://doi.org/10.1007/978-3-642-11928-6_18" - [context concept] - (assert (context? context) - "First argument must be a formal context.") - (assert (and (vector? concept) - (= 2 (count concept)) - (concept? context concept)) - "Second argument must be a formal concept of the given context.") - (let [[extent intent] concept - c-inc (* (count extent) (count intent)) - g-inc (reduce + - (map - #(count (object-derivation context #{%})) - extent)) - a-inc (reduce + - (map #(count (attribute-derivation context #{%})) - intent)) - o-inc (- (+ g-inc a-inc) - c-inc)] ; is at least c-inc large - (/ c-inc o-inc))) - -(def ^:dynamic *fast-computation* - "Enable computation of concept probability with floating point arithmetic - instead of rationals" - nil) - -(defn concept-probability - "Compute the probability of a `concept' in `context' 𝕂 in the following manner. - Let pₘ be the relative frequence of attribute m in context. The - probability of a subset B ⊆ M in 𝕂 is the product of all pₘ for m ∈ B. - Then the probability of a concept is defined by pr(A,B) := pr(B=B'') - which is ∑_{k=0}^n {n choose k}·p_Bᵏ·(1-p_B)ⁿ⁻ᵏ·∏_{m ∈ M ∖ B}(1-p_mᵏ)." - [context concept] - (let [nr_of_objects (count (objects context)) - n (if *fast-computation* (double nr_of_objects) nr_of_objects) - M (attributes context) - B (second concept) ; intent of concept - P_M_B (mapv #(/ (count (attribute-derivation context #{%})) n ) (difference M B)) - p_B (r/fold * (map #(/ (count (attribute-derivation context #{%})) n) B)) - one_minus_p_B_n (expt (- 1 p_B) n)] - (if (not= (double p_B) 1.0) ;; if concept's extent= n - (loop [k 1 ;; since for k=0 the last term is 0, we can start with 1 - result 0 - binomial n ;; since k=0 the start binomial is n - p_B_k p_B - one_minus_p_B_k (/ one_minus_p_B_n (- 1 p_B)) - P_M_B_k P_M_B ] - (if (or (== k n) (== p_B_k 0)) ;; either done or underflowed probability (double) - result - (let [new_res - (* binomial p_B_k one_minus_p_B_k - (r/fold * (map #(- 1 %) P_M_B_k)))] - (recur - (inc k) - (+ new_res result) - (* binomial (/ (- n k) (inc k))) - (* p_B_k p_B) - (/ one_minus_p_B_k (- 1 p_B)) - (mapv (partial *) P_M_B_k P_M_B))))) - 1))) - - -;;; Robustness of Concepts - -(defn- concept-robustness-add-next-entry - "Helper-function for `concept-robustness-polynomial'. - - This function computes the value e(Y,`concept'), based on the already computed - values e(Z,`concept'), which are given in the second parameter `cache' in the - form [Z, e(Z, `concept')]. - - This function is needed in the algorithm on page 19 in \"Finding Robust - Itemsets under Subsampling\" from Tatti, Moerchen, and Calders." - [concept cache] - (let [newvalue (reduce - (fn [x V] (- x (second V))) - 0 - (filter #(subset? (second (first %)) (second concept)) - cache))] - (conj cache [concept, newvalue]))) - -(defn concept-robustness-polynomial - "Return the coefficients of the robustness polynomial of `concept'. - - For the given `concept' of a context, the coefficients of the polynomial p - corresponding to the robustness is computed by using the seq `concepts' of - all concepts of the context. The optional boolean parameter `sorted?' allows - to declare the seq of concepts as being already sorted by increasing - attribute-set. Thus if v is the result of (robustness-polynomial concept - concepts), then (eval-polynomial v (- 1 alpha)) computes the robustness with - parameter alpha. - - For details see \"Finding Robust Itemsets under Subsampling\" from Tatti, - Moerchen, and Calders, pages 17–19." - ([concept concepts sorted?] - (let [B (second concept) - used-concepts (drop 1 (if sorted? - (filter #(subset? B (second %)) concepts) - (sort-by #(count (second %)) - (filter #(subset? B (second %)) - concepts)))) - ;; store for all subconcepts (C_A,C_B) of concept the vector [C, e(C_B, concept)] - concepts-with-values (reduce - (fn [x y] - (concept-robustness-add-next-entry y x)) - [[concept, 1]] - used-concepts) - sup (count (first concept))] - ;; use the above computed values [C, e(C_B, concept)] to compute the polynomial - (reduce - (fn [old-coefficients entry] - (let [index (- sup (count (first (first entry))))] - (assoc old-coefficients - index (+ (nth old-coefficients index) (second entry))))) - (vec (take (+ 1 sup) (repeat 0))) - concepts-with-values))) - ([concept concepts] - (concept-robustness-polynomial concept concepts false))) - -(defn concept-robustness - "Computes the robustness of a `concept' in a context with parameter `alpha' by - using the seq `concepts' consisting of all concepts of the context. The - optional boolean parameter `sorted?' allows to declare the seq of concepts as - beeing already sorted by increasing size of the attribute set. This function - uses the function concept-robustness-polynomial." - ([concept concepts alpha sorted?] - (assert (and (number? alpha) - (<= 0 alpha 1)) - "Third argument must be between 0 and 1!") - (eval-polynomial (concept-robustness-polynomial concept concepts sorted?) (- 1 alpha))) - ([concept concepts alpha] - (concept-robustness concept concepts alpha false))) - -(defn average-concept-robustness - "Takes the seq `concepts' consisting of all concepts of a context and computes - the average concept robustness with parmater `alpha'." - [concepts alpha] - (assert (and (number? alpha) - (<= 0 alpha 1)) - "Second argument must be between 0 and 1!") - (let [sorted-concepts (sort-by - #(count (second %)) - concepts) - n (count sorted-concepts) - robustness-values (map - #(concept-robustness - (nth sorted-concepts %) - (drop % sorted-concepts) - alpha - true) - (range 0 n))] - (/ (reduce + robustness-values) n))) - - -;;; Similarity Measures for Concepts (implemented by Anselm von Wangenheim) - -(defn jaccard-index - "Computes the Jaccard index of two sets. This is |x ∩ y| / |x ∪ y|. - Returns 1 if both sets are empty." - [x y] - (if (and (empty? x) (empty? y)) - 1 - (/ (count (intersection x y)) (count (union x y))))) - -(defn sorensen-coefficient - "Computes the Sorensen coefficient of two sets. - This is 2 * |x ∩ y| / (|x| + |y|). - Returns 1 if both sets are empty." - [x y] - (if (and (empty? x) (empty? y)) - 1 - (/ (* 2 (count (intersection x y))) (+ (count x) (count y))))) - -(defn weighted-concept-similarity - "Computes a weighted concept similarity for a given similatity measure `sim', - two concepts [`c1' `c2'] and an optional weight `w' (default is 1/2). - - That is the weighted average of the similarity of the extents/object sets - (weight `w') and the intents/attribute sets (weight 1-`w'). - - This is from Alqadah, F. & Bhatnagar, R. (2011), 'Similarity measures in - formal concept analysis.', Ann. Math. Artif. Intell. 61 (3), 249, - https://doi.org/10.1007/s10472-011-9257-7" - ([sim [c1 c2]] (weighted-concept-similarity sim [c1 c2] (/ 1 2))) - ([sim [c1 c2] w] - (assert (and (number? w) - (<= 0 w 1)) - "Thrid argument must be between 0 and 1!") - (+ - (* w (sim (c1 0) (c2 0))) - (* (- 1 w) (sim (c1 1) (c2 1)))))) - - - -;;; Concept stability - -(defn mcs-stability-approximation - "Approximates concept stability with Markov Chains." - [ctx concept sample-size] - (let [counter (atom 0)] - (doall - (for [i (range sample-size)] - (let [prem (first concept) - concl (second concept) - limit (count concl)] - (if (= (attribute-derivation ctx - (take (rand-int limit) - (shuffle concl))) - prem) - (swap! counter inc))))) - (/ @counter sample-size))) - -(defn lds-stability-approximation - "Approximates concept stability with Low-Discrepancy Sampling. The function - takes a context and concept, the sample-size and base (both as integer). - An additional argument may be given to choose the sampling method. - The options are: - :sobol One-dimensional Sobol Sequence (default) - :svdc Scrambled Van der Corput Sequence - - Function based on 'An Efficient Approximation of Concept - Stability Using Low-Discrepancy Sampling' Ibrahim; Missaoui 2018 - https://link.springer.com/chapter/10.1007/978-3-319-91379-7_3 " - ([ctx concept sample-size base] - (lds-stability-approximation ctx concept sample-size base :sobol)) - ([ctx concept sample-size base sampling-method] - (let [lds (atom []) - counter (atom 0) - intent (second concept) - intent-size (count intent) - powerset (subsets intent)] - (doall - (for [i (range sample-size)] - (swap! lds conj (case sampling-method - :sobol (generate-sobol i) - :svdc (generate-svdc i base) - (generate-sobol i))))) - (doall - (for [element @lds] - (let [position (int (+ (* intent-size element) 0.5)) - subset (nth powerset position)] - (if (= (first concept) - (attribute-derivation ctx subset)) - (swap! counter inc))))) - (/ @counter sample-size)))) - -;;; standard lattice properties to some degree - -(defn satisfying-triples - "Given lattice lat, compute triples (a,b,c)∈L³ (pairwise different) - such that they fullfil a given condition. The triples may be - filtered beforehand using prefilter." - ([^Lattice lat condition] - (let [base (into [] (lattice-base-set lat))] - ;; (filter condition (filter prefilter (permuted-combinations base 3))))) - (filter condition (permuted-combinations base 3)))) - ([lat condition prefilter] - (let [base (into [] (lattice-base-set lat))] - (filter condition (filter prefilter (permuted-combinations base 3)))))) - - -(defn distributive-triples - "Given lattice lat, compute triples (x,y,z)∈L³ (pairwise different) - such that they fullfil the distributive property - x∨(y∧z)=(x∨y)∧(x∨z)." - ([^Lattice lat] - (distributive-triples lat (fn [x] true))) - ([^Lattice lat prefilter] - (let [inf (inf lat), - sup (sup lat)] - (satisfying-triples lat (fn [[x y z]] - (= (sup x (inf y z )) - (inf (sup x y) (sup x z)))) - prefilter)))) - -(defn modular-triples - "Given lattice lat, compute triples (x,y,z)∈L³ (pairwire different) - such that they fullfil the modular property x ≤ z ⇒ - x∨(y∧z)=(x∨y)∧z." - ([lat] - (modular-triples lat (fn [x] true))) - ([lat prefilter] - (let [inf (inf lat), - sup (sup lat), - ord (lattice-order lat) - base (into [] (lattice-base-set lat))] - (satisfying-triples lat (fn [[x y z]] - (if (ord x z) ;; if x≤y - (= ;; check x∨(y∧z)=(x∨y)∧z - (sup x (inf y z)) - (inf (sup x y) z)) - true)) - prefilter)))) ;; else always true - -(defn distributivity-degree - "Computes the number of triples (a,b,c)∈L³ (pairwise different) - that fullfil the distributivity law and divides it by the number of - possible pw different triples." - [lat] - (let [n (count (lattice-base-set lat))] - (if (< n 3) - 1 ;; in case we have less than 3 elements we have distributivity - (/ (count (distributive-triples lat)) - (* 6 (binomial-coefficient n 3)))))) - -(defn modularity-degree - "Computes the number of triples (a,b,c)∈L³ (pairwise different) - that fullfil the modularity law and divides it by the number of - possible pw different triples. (tbc later on)" - [lat] - (let [n (count (lattice-base-set lat))] - (if (< n 3) - 1 ;; in case we have less than 3 elements we have modularity - (/ (count (modular-triples lat)) - (* 6 (binomial-coefficient n 3)))))) - -(defn elements-distributivity - "Computes the number of triples (a,b,c)∈L³ (pw different) where either - a=e, b=e, or c=e, that fullfil the modularity law. This number is - then divided it by the number of possible pw different triples of such kind." - [lat e] - (assert (contains? (lattice-base-set lat) e)) - (let [n (count (lattice-base-set lat)), - filterfunc (fn [[x y z]] (or (= x e) (= y e) (= z e)))] - (/ (count (distributive-triples - lat filterfunc)) - (* 6 (binomial-coefficient (- n 1) 2))))) - -(defn elements-modularity - [lat e] - (assert (contains? (lattice-base-set lat) e)) - (let [n (count (lattice-base-set lat))] - (/ (count (modular-triples lat (fn [[x y z]] (or (= x e) (= y e) (= z e))))) - (* 6 (binomial-coefficient (- n 1) 2))))) - -;;; Relevant Attributes (Objects) et Al - -(defn attribute-information-entropy - "Computes the attribute-information-entropy for a given context 𝕂using the formula - (∑_{m ∈ M} 1-{m}''/|M|)/|M|, see https://doi.org/10.1007/978-3-030-23182-8_8" - [ctx] - (let [M (attributes ctx) - nr_of_attributes (count M)] - (/ (- nr_of_attributes - (r/fold + (pmap - (fn [m] (/ (count (context-attribute-closure ctx #{m})) - nr_of_attributes)) - M))) - nr_of_attributes))) - -(defn object-information-entropy - "Computes the object-information-entropy for a given context 𝕂using the formula - (∑_{g ∈ G} 1-{g}''/|G|)/|G|, see https://doi.org/10.1007/978-3-030-23182-8_8" - [ctx] - (attribute-information-entropy (dual-context ctx))) - -(defn information-entropy - "Computes the mean entropy of context ctx based on the equal - weighted sum of attribute-information-entropy and - object-information-entropy." - [ctx] - (/ (+ (attribute-information-entropy ctx) (object-information-entropy ctx)) 2)) - - -(defn shannon-attribute-information-entropy - "Computes the Shannon-attribute-information-entropy for a given context 𝕂using the formula - ∑_{m ∈ M} -{m}''/|M|· log₂ ({m}''/|M|), see https://doi.org/10.1007/978-3-030-23182-8_8" - [ctx] - (let [M (attributes ctx) - nr_of_attributes (count M)] - (r/fold + (pmap (fn [x] (- (* x (log2 x)))) - (pmap - (fn [m] (/ (count (context-attribute-closure ctx #{m})) - nr_of_attributes)) - M))))) - -(defn shannon-object-information-entropy - "Computes the Shannon-object-information-entropy for a given context 𝕂using the formula - ∑_{g ∈ G} -{g}''/|G|· log₂ ({g}''/|G|), see https://doi.org/10.1007/978-3-030-23182-8_8" - [ctx] - (shannon-attribute-information-entropy (dual-context ctx))) - -(defn shannon-attribute-information-entropy-fast - "Computes the Shannon-attribute-information-entropy for a given - context 𝕂using the formula ∑_{m ∈ M} -{m}''/|M|· log₂ ({m}''/|M|), - see https://doi.org/10.1007/978-3-030-23182-8_8. This implementation - resorts to bit vectors in order to increase the computation - speed. This conversion is not adviced for small data sets. " - [ctx] - (with-binary-context ctx - (let [a-closure-counts - (pmap (fn [y] - (let [^BitSet bs (BitSet.)] - (.set bs y) - (bitwise-context-attribute-closure - incidence-matrix - object-count - attribute-count - bs))) - (range attribute-count))] - (- - (r/fold + (map (fn [x] (* (/ (.cardinality ^BitSet x) ^long attribute-count) - (log2 (/ (.cardinality ^BitSet x) ^long attribute-count)))) - a-closure-counts)))))) - - -(defn shannon-object-information-entropy-fast - "Computes the Shannon-object-information-entropy for a given context 𝕂using the formula - ∑_{g ∈ G} -{g}''/|G|· log₂ ({g}''/|G|), see https://doi.org/10.1007/978-3-030-23182-8_8" - [ctx] - (shannon-attribute-information-entropy-fast (dual-context ctx))) - -(defn shannon-information-entropy - "Computes the mean shannon-entropy of context ctx based on the equal - weighted sum of attribute-information-entropy and - object-information-entropy." - [ctx] - (/ (+ (shannon-attribute-information-entropy ctx) - (shannon-object-information-entropy ctx)) 2)) - -(defn shannon-information-entropy-fast - "Computes the mean shannon-entropy of context ctx based on the equal - weighted sum of attribute-information-entropy and - object-information-entropy." - [ctx] - (/ (+ (shannon-attribute-information-entropy-fast ctx) - (shannon-object-information-entropy-fast ctx)) 2)) - -(defn extent-label-function - "Computes the label for given g ∈ G, i.e., the natural number n such - that n=|{c ∈ 𝔅(𝕂) ∣ g ∈ ext(c)}|, see - https://doi.org/10.1007/978-3-030-23182-8_8" - ([ctx g] - (extent-label-function ctx (concepts :in-close ctx) g)) - ([ctx concepts g] - (count - (filter (fn [x] (contains? (first x) g)) - concepts)))) - -(defn intent-label-function - "Computes the label for given m ∈ M, i.e., the natural number n such - that n=|{c ∈ 𝔅(𝕂) ∣ m ∈ int(c)}|, see - https://doi.org/10.1007/978-3-030-23182-8_8" - ([ctx m] - (extent-label-function ctx (concepts :in-close ctx) m)) - ([ctx concepts m] - (count - (filter (fn [x] (contains? (second x) m)) - concepts)))) - -(defn attribute-removal-robust-concepts - "Computes the set of concepts {c ∈ 𝔅(𝕂) ∣ (int(c) ∖ A)' = ext(c)} - for some attribute set A ⊆ M." - ([ctx A] - (attribute-removal-robust-concepts ctx (concepts :in-close ctx) A)) - ([ctx theconcepts A] - (into [] (r/filter (fn [x] (= - (attribute-derivation ctx (difference (second x) A)) - (first x))) - theconcepts)))) - -(defn object-removal-robust-concepts - "Computes the set of concepts {c ∈ 𝔅(𝕂) ∣ (ext(c) ∖ A)' = int(c)} - for some attribute set A ⊆ G." - ([ctx A] - (object-removal-robust-concepts ctx (concepts :in-close ctx) A)) - ([ctx theconcepts A] - (into [] (r/filter (fn [x] (= - (object-derivation ctx (difference (first x) A)) - (second x))) - theconcepts)))) - - -(defn relative-relevance - "Computes for formal context (G,M,I) the relative relevance of - attribute set A ⊆ M, using the formula from Proposition 3.5 in - https://doi.org/10.1007/978-3-030-23182-8_8, i.e., - r(A)=1-∑_{c∈𝔅(𝕂_A)}|ext(c)|/∑_{c∈𝔅(𝕂)}|ext(c)|, - where 𝔅(𝕂_A)={c∈𝔅(𝕂)∣(int(c)∖A)'=ext(c)}" - ([ctx A] - (relative-relevance ctx (concepts :in-close) A)) - ([ctx theconcepts A] - (let [extsum (r/fold + (map (fn [x] (count (first x))) theconcepts))] - (- 1 - (->> theconcepts - (filter - (fn [x] (= (count - (attribute-derivation ctx (difference (second x) A))) - (count (first x))))) - (pmap (fn [x] (count (first x)))) - (r/fold +) - (* (/ 1 extsum))) - )))) - -(defn relative-relevance-fast - "Compute relative-relevance using bitsets" - [ctx theconcepts A] - (with-binary-context ctx - (let [o-prime (partial bitwise-object-derivation incidence-matrix object-count attribute-count) - a-prime (partial bitwise-attribute-derivation incidence-matrix object-count attribute-count) - theextents (pmap (fn [x] (to-bitset object-vector (first x))) theconcepts) - theatts (to-bitset attribute-vector A)] - (- 1 - (/ - (r/fold + (map (fn [x] - (if (= - (let [thing (o-prime x)] - (.andNot thing theatts) ;; remove attribute set - (.cardinality (a-prime thing))) - (.cardinality x)) - (.cardinality x) - 0)) - theextents)) - (r/fold + (map (fn [x] (.cardinality x)) theextents))))))) - -(defn next-maximal-relevant - "Given a formal context (G,M,I), an attribute set A ⊆ M, this - functions computes the most relevant m ∈ M ∖ A with respect to relative-relevance." - ([ctx theconcepts] (next-maximal-relevant ctx theconcepts #{})) - ([ctx theconcepts A] - (let [atts (attributes ctx) - available-atts (difference atts A) - obs (objects ctx)] - (apply max-key (fn [x] (relative-relevance-fast ctx theconcepts (union A #{x}))) - available-atts)))) - -(defn next-n-maximal-relevant - "Based on next-maximal-relevant, compute the the next n maximal - relevant features in a consekutive manner. Please be advised, this - is not necessiraly equivalent to compute the subset N ⊆ M with |N|=n - being the most relevant wrt relative-relevance." - ([ctx theconcepts n] - (next-n-maximal-relevant ctx theconcepts n #{})) - ([ctx theconcepts n A] - (loop [[counter resultset] [0 []]] - (if (< counter n) - (recur [(inc counter) - (conj resultset - (next-maximal-relevant ctx theconcepts (set (union resultset A))))]) - resultset)))) - -(defn n-maximal-relevant - "Based on relative-relevance, compute the the subset N ⊆ M with |N|=n, - such that there is no L ⊆ M with r(N) k n) - result - (recur - (inc k) - (conj result - (let [atts (attributes ctx) - available-atts (difference atts (union A result)) - obs (objects ctx)] - (apply max-key (fn [x] - (let [pctx (make-context obs (union #{x} result A) (incidence ctx))] - (* - (count (concepts :in-close pctx)) - (object-information-entropy pctx)))) - available-atts))))))) - -(defmethod next-n-maximal-relevant-approx :shannon - ([_ ctx n] - (next-n-maximal-relevant-approx :shannon ctx n #{})) - ([_ ctx n A] - (loop [k 1 - result []] - (if (> k n) - result - (recur - (inc k) - (conj result (let [atts (attributes ctx) - available-atts (difference atts (union A result)) - obs (objects ctx)] - (apply max-key (fn [x] - (let [pctx (make-context obs (union #{x} A result) (incidence ctx))] - (* - (count (concepts :in-close pctx)) - (shannon-object-information-entropy-fast pctx)))) - available-atts)))))))) - - -(defn nRandomAtts - [ctx n] - (let [atts (attributes ctx)] - (take n (shuffle atts)))) - -;; (defn rel-consistency ??? -;; "Computes the relative consistency of a subset $N ⊆ M$ with respect to -;; a given formal context (G,M,I), and some attribute subset N ⊆ M" -;; [ctx N] -;; (let [G (objects ctx) -;; M (attributes ctx) -;; MN (difference M N) -;; ctx-N (make-context G N (incidence ctx)) -;; ctx-MN (make-context G MN (incidence ctx))] -;; (let [derive-N (fn [x] (context-object-closure ctx-N x)) -;; derive-MN (fn [x] (context-object-closure ctx-MN x))] -;; (/ -;; (count (filter (fn [x] (subset? (derive-N #{x}) (derive-MN #{x}))) G)) -;; (count G) -;; )))) - -;; ) - - -(defn generate-from-triple [triple lat] - - (let [stage1-meets (for [a triple b triple] (inf lat a b)) - stage1-joins (for [a triple b triple] (sup lat a b)) - - stage2-meets (for [a stage1-joins b stage1-joins] (inf lat a b)) - stage2-joins (for [a stage1-meets b stage1-meets] (sup lat a b)) - - final-meet (inf lat stage1-joins) - - ground-set (set/union stage1-meets - stage1-joins - stage2-meets - stage2-joins - final-meet) - order-function ;tbt - ] -;; Copyright ⓒ the conexp-clj developers; all rights reserved. -;; The use and distribution terms for this software are covered by the -;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) -;; which can be found in the file LICENSE at the root of this distribution. -;; By using this software in any fashion, you are agreeing to be bound by -;; the terms of this license. -;; You must not remove this notice, or any other, from this software. - -(ns conexp.fca.metrics - (:require [clojure.core.reducers :as r] - [clojure.math.combinatorics :refer [permuted-combinations combinations]] - ;; [clojure.math.numeric-tower :refer [log]] - [conexp.base :refer :all] - [conexp.math.markov :refer :all] - [conexp.fca - [contexts :refer [make-context incidence dual-context - attribute-derivation - context-attribute-closure - context-object-closure - object-derivation random-context - objects attributes - context? concept? - adiag-context - rand-context]];temp + context? concept?]] [exploration :refer :all] [fast :refer [with-binary-context to-bitset @@ -841,7 +28,14 @@ bitwise-object-derivation bitwise-attribute-derivation concepts]] [implications :refer :all] - [lattices :refer [inf sup lattice-base-set make-lattice concept-lattice lattice-order]]] + [lattices :refer [inf + sup + lattice-base-set + make-lattice + make-lattice-nc + concept-lattice + lattice-order + distributive?]]] [conexp.math.util :refer [eval-polynomial binomial-coefficient]]) (:import [conexp.fca.lattices Lattice] [java.util ArrayList BitSet])) @@ -1601,7 +795,7 @@ ;; ) ;returns destributive lattice generated by the concepts in "triple" -;tripe must be a collection of three concepts in "lat" +;triple must be a collection of three concepts in "lat" (defn generate-from-triple [triple lat] (let [stage1-meets (set (filter some? (for [a triple b triple] (if (not= a b) ((inf lat) a b))))) @@ -1643,7 +837,7 @@ ) ) -;retruns all complement of "concept" in "lat" +;retruns all complements of "concept" in "lat" (defn element-complement [concept lat] (let [base-set (lattice-base-set lat) top (first(filter #(= (second %) #{}) base-set)) @@ -1657,59 +851,9 @@ base-set)) ) -;returns all decompositions pair of "lat" for Libkin decompositions -(defn decompositions [lat] - (let [neutral-elements (neutral-concepts lat)] - (for [n neutral-elements c (element-complement n lat)] [n c]) -)) - - - - - - -;meets: -x-y -x-z -y-z -x-y-z - -x+y-x+z -x+y-y+z -x+z-y+z - -;joins: -x+y -x+z -y+z -x+y+z - -x-y+x-z -x-y+y-z -x-z+y-z - -x-y+x-z+y-z - -;test -(def ctx (make-context #{1 2 3 4 5} - #{"A" "B" "C" "D" "E"} - #{[1 "A"] [2 "A"] [2 "B"] [3 "B"] [3 "C"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) -(def lat (concept-lattice ctx)) - - -(def ctx2 (make-context #{1 2 3 4 5} - #{"A" "B" "C" "D" "E"} - #{[1 "A"] [2 "A"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) -(def lat2 (concept-lattice ctx)) - - -(def ctx3 (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] - [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] - [7 "A"] [7 "B"] [7 "C"]})) -(def lat3 (concept-lattice ctx3)) ;;; - nil +nil From 9f564e3bf4b4d74411bd4f86aeaec71d8523da75 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 21 Sep 2023 18:41:58 +0200 Subject: [PATCH 070/117] Cleanup and Documentation. --- doc/LibkinDecomposition.org | 632 ++++++++++++++++++ .../clojure/conexp/fca/decompositions.clj | 71 +- 2 files changed, 661 insertions(+), 42 deletions(-) create mode 100644 doc/LibkinDecomposition.org diff --git a/doc/LibkinDecomposition.org b/doc/LibkinDecomposition.org new file mode 100644 index 000000000..e3a0e9067 --- /dev/null +++ b/doc/LibkinDecomposition.org @@ -0,0 +1,632 @@ +#+property: header-args :wrap src text +#+property: header-args:text :eval never + +* Libkin Decomposition + +~conexp-clj~ allows for the computation of Libkin Decompositions of lattices. +For an explanation of the concept consult "Direct product decompositions of lattices, closures and relation schemes" by Leonid Libkin + +We will consider the following lattice as an example: + +#+begin_src clojure :exports both +(def ctx (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] + [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] + [7 "A"] [7 "B"] [7 "C"]})) +(def lat (concept-lattice ctx)) +#+end_src + +** Creating Formal Contexts + +~conexp-clj~ lets you easily create formal contexts in a number of ways. We +shall describe some of them in the following. + +A context ~(G,M,I)~ consists of two sets G and M and an incidence realtion I ⊆ +G×M. G is a set of /objects/, M is a set of /attributes/ and ~gIm~ (short for +(g,m) ∈ I) can be read as /g has the attribute m/. To create a context you only +have to define these sets. There a (at least) three options: + +*** Using a defined relation + +The fasted way to construct a formal context is just by writing it down, as in the following example. + +#+begin_src clojure :results silent +(def ctx-1 (make-context [1 2 3] [1 2 3] <=)) +#+end_src + +To see the formal context, just evaluate its variable explicitly + +#+begin_src clojure :exports both +ctx-1 +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 +--+------ +1 |x x x +2 |. x x +3 |. . x + +#+end_src + +*** Defining all sets explicitly + +A formal context can also be specified by directly listing the incidence +relation (using Clojure's own syntax for sets and tuples): + +#+begin_src clojure :exports both +(def ctx-2 (make-context #{1 2 3 4 5 6} + #{1 2 3 4 5 6} + #{[1 1] [1 2] [1 3] [1 5] + [1 6] [2 2] [2 5] [3 3] + [3 6] [4 4] [4 5] [4 6] + [5 5] [6 6]})) +ctx-2 +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 4 5 6 +--+------------ +1 |x x x . x x +2 |. x . . x . +3 |. . x . . x +4 |. . . x x x +5 |. . . . x . +6 |. . . . . x + +#+end_src + +One can enter the cross-table explicitly, using the function +~make-context-from-matrix~, like this + +#+begin_src clojure :exports both +(def ctx-3 (make-context-from-matrix 6 6 + [1 1 1 0 1 1 + 0 1 0 0 1 0 + 0 0 1 0 0 1 + 0 0 0 1 1 1 + 0 0 0 0 1 0 + 0 0 0 0 0 1])) +ctx-3 +#+end_src + +#+RESULTS: +#+begin_src text + |0 1 2 3 4 5 +--+------------ +0 |x x x . x x +1 |. x . . x . +2 |. . x . . x +3 |. . . x x x +4 |. . . . x . +5 |. . . . . x + +#+end_src + +Here, instead of writing out the sets of objects and attributes explicitly, we +have just entered their cardinality ~6~. With this, the set of objects and +attributes automatically gets set to ~#{1 2 3 4 5 6}~. From time to time, this +make save some typing time. + +### Using a custom function + +This will create a formal context with G = M = {1,2,3,4,5,6} and (n,m) in I if +and only if gcd(n,m) = 1: + +#+begin_src clojure :exports both +(def ctx-4 (make-context [1 2 3 4 5 6] + [1 2 3 4 5 6] + (fn [x y] + (= 1 (gcd x y))))) +ctx-4 +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 4 5 6 +--+------------ +1 |x x x x x x +2 |x . x . x . +3 |x x . x x . +4 |x . x . x . +5 |x x x x . x +6 |x . . . x . + +#+end_src + + +*** Creating Random Contexts + +For some experiments it is often helpful to randomly create contexts. Here is +how this can be done in conexp-clj. Of course, the exact result is probably not +the one you see here + +#+begin_src clojure :exports both +(rand-context #{1 2 3} 0.5) +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 +--+------ +1 |x x x +2 |x x . +3 |x . x + +#+end_src + +Here, the first parameter is the set of objects and attributes and the second +parameter is the probality for the incidence. + +** Working with Formal Contexts + +Having created a formal context, there a plenty of possibilities to work with +it. + +*** Basic Accessors + +The most basic operation on formal contexts is to retrieve its components. This +can be done as follows + +#+begin_src clojure :exports both +[(objects ctx-2), (attributes ctx-2), (incidence ctx-2)] +#+end_src + +#+RESULTS: +#+begin_src text +[#{1 4 6 3 2 5} + #{1 4 6 3 2 5} + #{[2 2] [2 5] [3 3] [1 1] [6 6] [4 6] [1 3] [1 5] [5 5] [3 6] [4 5] + [1 6] [4 4] [1 2]}] +#+end_src + +*** Clarifying and Reducing Contexts + +To see if ~ctx-2~ is clarified, you can use the functions ~object-clarified?~, +~attribute-clarified?~, and ~context-clarified?~. + +#+begin_src clojure :exports both +[(object-clarified? ctx-2), + (attribute-clarified? ctx-2), + (context-clarified? ctx-2)] +#+end_src + +#+RESULTS: +#+begin_src text +[true true true] +#+end_src + +If ~ctx-2~ would not be clarified, one could obtain a clarified version of it by +using + +#+begin_src clojure :eval never :exports code +(clarify-attributes ctx-2) +(clarify-objects ctx-2) +(clarify-context ctx-2) +#+end_src + +As another example, for ~ctx-2~, we could for instance compute the arrow +relations (e.g. to see which objects or attributes are irreducible) + +#+begin_src clojure :exports both +[(up-arrows ctx-2), (down-arrows ctx-2)] +#+end_src + +#+RESULTS: +#+begin_src text +[#{[4 3] [6 3] [4 2] [6 5] [5 2] [1 4] [5 6] [2 6] [3 5]} + #{[4 3] [2 3] [4 2] [4 1] [1 4] [3 1] [2 1] [2 6] [3 5] [3 2]}] +#+end_src + +To directly see whether ~ctx-2~ is reduced, use ~context-reduced?~, and to +obtain a reduced version of ~ctx-2~, call ~reduce-context~ like so: + +#+begin_src clojure :exports both +(reduce-context ctx-2) +#+end_src + +#+RESULTS: +#+begin_src text + |2 3 4 5 6 +--+---------- +1 |x x . x x +2 |x . . x . +3 |. x . . x +4 |. . x x x + +#+end_src + +*** Derivation Operations + +Now I want to get all objects, which attribute ~1~ and ~2~ have in common + +#+begin_src clojure :exports both +(attribute-derivation ctx-2 #{1 2}) +#+end_src + +#+RESULTS: +#+begin_src text +#{1} +#+end_src + +The same can be done for sets of objects + +#+begin_src clojure :exports both +(object-derivation ctx-1 #{1 2}) +#+end_src + +#+RESULTS: +#+begin_src text +#{3 2} +#+end_src + +Instead of using this long function names, there are also the abbreviations +~aprime~ and ~oprime~ available. + +If you want to compute the closure of a given set of objects or attributes in +our context use + +#+begin_src clojure :exports both +[ (context-attribute-closure ctx-2 #{1 2}), + (context-object-closure ctx-2 #{1 2}) ] +#+end_src + +#+RESULTS: +#+begin_src text +[#{1 6 3 2 5} #{1 2}] +#+end_src + +*** Formal Concepts and Concept Lattices + +We can compute all intents and extents via + +#+begin_src clojure :exports both +[(extents ctx-2), (intents ctx-2)] +#+end_src + +#+RESULTS: +#+begin_src text +[(#{} + #{4} + #{1} + #{1 4} + #{1 2} + #{1 3} + #{1 4 2 5} + #{1 4 6 3} + #{1 4 6 3 2 5}) + (#{} + #{5} + #{2 5} + #{6} + #{6 5} + #{6 3} + #{4 6 5} + #{1 6 3 2 5} + #{1 4 6 3 2 5})] +#+end_src + +To get all formal concepts use + +#+begin_src clojure :exports both +(concepts ctx-2) +#+end_src + +#+RESULTS: +#+begin_src text +([#{1 4 6 3 2 5} #{}] + [#{1} #{1 6 3 2 5}] + [#{} #{1 4 6 3 2 5}] + [#{4} #{4 6 5}] + [#{1 4 6 3} #{6}] + [#{1 3} #{6 3}] + [#{1 4} #{6 5}] + [#{1 2} #{2 5}] + [#{1 4 2 5} #{5}]) +#+end_src + +If you are only interested in the number of formal concepts, you can instead +just ~count~ the concepts, like so + +#+begin_src clojure :exports both +(count (concepts ctx-2)) +#+end_src + +#+RESULTS: +#+begin_src text +9 +#+end_src + +This can be combined neatly with ~map~ to get the number of concepts for all the +formal contexts we have defined to far + +#+begin_src clojure :exports both +(map (comp count concepts) [ctx-1 ctx-2 ctx-3 ctx-4]) +#+end_src + +#+RESULTS: +#+begin_src text +(3 9 9 8) +#+end_src + +The standard ~comp~ functions implements function composition in Clojure. + +Finally, you can compute the concept lattice using the ~concept-lattice~ +function like so: + +#+begin_src clojure :exports both +(concept-lattice ctx-2) +#+end_src + +#+RESULTS: +#+begin_src text +Lattice on 9 elements. +#+end_src + +Note that this will not give you a picture of the lattice, but a representation +of the algebraic structure. + +*** Canonical Base + +You get the canonical base with (who would have guessed that!) + +user=> (canonical-base ctx-1) +#{(#{b} ==> #{e}) (#{c} ==> #{f}) (#{c f e} ==> #{a b}) + (#{a} ==> #{c b f e}) (#{d} ==> #{f e}) (#{b f e} ==> #{a c})} + +The ~canonical-base~ function can take additional arguments like background +knowledge and filter predicates. See the documentation of this function for +further details: + +#+begin_src clojure :exports both +(doc canonical-base) +#+end_src + +#+RESULTS: +#+begin_src text +------------------------- +conexp.fca.implications/canonical-base +([ctx] [ctx background-knowledge] [ctx background-knowledge predicate]) + Returns the canonical base of given context, as a lazy sequence. Uses + «background-knowledge» as starting set of implications, which will not appear + in the result. If «predicate» is given (a function), computes only those + implications from the canonical base whose premise satisfy this predicate, + i.e. «predicate» returns true on these premises. Note that «predicate» has to + satisfy the same conditions as the predicate to «next-closed-set-in-family». +nil +#+end_src + +*** Further Operations + +There a several further operations you can do with contexts, e.g., the context +apposition, context subposition, and more. For illustration, let us define two +contexts: + +#+begin_src clojure :exports both +(def ctx-5 (make-context #{1 2 3} #{1 2 3} <)) +(def ctx-6 (make-context-from-matrix [1 2 3] + ['a 'b 'c 'd] + [1 1 0 1 + 1 0 1 0 + 0 0 1 1])) +[ctx-5 ctx-6] +#+end_src + +#+RESULTS: +#+begin_src text +[ |1 2 3 +--+------ +1 |. x x +2 |. . x +3 |. . . + |a b c d +--+-------- +1 |x x . x +2 |x . x . +3 |. . x x +] +#+end_src + +The apposition of these two contexts is + +#+begin_src clojure :exports both +(context-apposition ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |[1 0] [2 0] [3 0] [a 1] [b 1] [c 1] [d 1] +--+------------------------------------------ +1 |. x x x x . x +2 |. . x x . x . +3 |. . . . . x x + +#+end_src + +Note how the two sets of attributes are automatically made disjoint by +considering pairs with different second entry. + +Context apposition is a partial operation, as the contexts must have the same +set of objects. The following would not work: + +#+begin_src clojure :exports both +(context-apposition ctx-1 ctx-2) +#+end_src + +#+RESULTS: +#+begin_src text +class java.lang.IllegalArgumentExceptionclass java.lang.IllegalArgumentExceptionIllegalArgumentException Cannot do context apposition, since object sets are not equal. conexp.base/illegal-argument (base.clj:280) +#+end_src + +To compute the dual context, use what you would expect to use: + +#+begin_src clojure :exports both +(dual-context ctx-5) +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 +--+------ +1 |. . . +2 |x . . +3 |x x . + +#+end_src + +Now we can build the subposition of ~ctx-5~ and the dual of ~ctx-6~ + +#+begin_src clojure :exports both +(context-subposition ctx-5 (dual-context ctx-6)) +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 +------+------ +[1 0] |. x x +[2 0] |. . x +[3 0] |. . . +[a 1] |x x . +[b 1] |x . . +[c 1] |. x x +[d 1] |x . x + +#+end_src + +If you want to invert a given context use + +#+begin_src clojure :exports both +(invert-context ctx-5) +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 +--+------ +1 |x . . +2 |x x . +3 |x x x + +#+end_src + +You can create a composition of two (suitable) contexts with + +#+begin_src clojure :exports both +(context-composition ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |a b c d +--+-------- +1 |x . x x +2 |. . x x +3 |. . . . + +#+end_src + +The union of two contexts is created by + +#+begin_src clojure :exports both +(context-union ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |a b c d 1 2 3 +--+-------------- +1 |x x . x . x x +2 |x . x . . . x +3 |. . x x . . . + +#+end_src + +Sum to contexts with + +#+begin_src clojure :exports both +(context-sum ctx-5 ctx-6) +#+end_src + +To compute the intersection of two contexts (which is essentially empty), use + +#+begin_src clojure :exports both +(context-intersection ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + | +--+ +1 | +2 | +3 | + +#+end_src + +The context product goes like this + +#+begin_src clojure :exports both +(context-product ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |[1 a] [2 a] [3 a] [1 b] [2 b] [3 b] [1 c] [2 c] [3 c] [1 d] [2 d] [3 d] +------+------------------------------------------------------------------------ +[1 1] |x x x x x x . x x x x x +[2 1] |x x x x x x . . x x x x +[3 1] |x x x x x x . . . x x x +[1 2] |x x x . x x x x x . x x +[2 2] |x x x . . x x x x . . x +[3 2] |x x x . . . x x x . . . +[1 3] |. x x . x x x x x x x x +[2 3] |. . x . . x x x x x x x +[3 3] |. . . . . . x x x x x x + +#+end_src + +If you want to do a context semiproduct + +#+begin_src clojure :exports both +(context-semiproduct ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |[1 0] [2 0] [3 0] [a 1] [b 1] [c 1] [d 1] +------+------------------------------------------ +[1 1] |. x x x x . x +[2 1] |. . x x x . x +[3 1] |. . . x x . x +[1 2] |. x x x . x . +[2 2] |. . x x . x . +[3 2] |. . . x . x . +[1 3] |. x x . . x x +[2 3] |. . x . . x x +[3 3] |. . . . . x x + +#+end_src + +Compute Xia's product + +#+begin_src clojure :exports both +(context-xia-product ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |[1 a] [2 a] [3 a] [1 b] [2 b] [3 b] [1 c] [2 c] [3 c] [1 d] [2 d] [3 d] +------+------------------------------------------------------------------------ +[1 1] |. x x . x x x . . . x x +[2 1] |. . x . . x x x . . . x +[3 1] |. . . . . . x x x . . . +[1 2] |. x x x . . . x x x . . +[2 2] |. . x x x . . . x x x . +[3 2] |. . . x x x . . . x x x +[1 3] |x . . x . . . x x . x x +[2 3] |x x . x x . . . x . . x +[3 3] |x x x x x x . . . . . . + +#+end_src diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index df76dc144..73c84c740 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -1,56 +1,43 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + (ns conexp.fca.decompositions (:require [conexp.base :refer :all] + [conexp.math.algebra :refer :all] [conexp.fca [contexts :refer :all] [metrics :refer :all] [lattices :refer :all] - [posets :refer :all]] - )) + [posets :refer :all]])) -;returns all decompositions pair of "lat" for Libkin decompositions -(defn libkin-decomposition-pairs [lat] +(defn libkin-decomposition-pairs + "Returns all decompositions pair of *lat* for Libkin decompositions" + [lat] (let [neutral-elements (neutral-concepts lat)] - (for [n neutral-elements c (element-complement n lat)] [n c]) -)) - - -(defn lattice-ideal [lat concept] - (let [base-set (lattice-base-set lat) - order (lattice-order lat) - new-base-set (filter #(order % concept) base-set)] - - (make-lattice-nc new-base-set - order - (inf lat) - (sup lat)) - -) -) - - -(defn libkin-decomposition-lattices [lat decomp-pair] - [(lattice-ideal lat (first decomp-pair)) - (lattice-ideal lat (last decomp-pair))] -) - - - + (for [n neutral-elements c (element-complement n lat)] [n c]))) -;test -(def ctx (make-context #{1 2 3 4 5} - #{"A" "B" "C" "D" "E"} - #{[1 "A"] [2 "A"] [2 "B"] [3 "B"] [3 "C"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) -(def lat (concept-lattice ctx)) +(defn libkin-decomposition-lattices + "Computes the Lattices Resulting from the Libkin-Decomposition on the + Providen Decomposition Pair." + [lat decomp-pair] + (let [set1 (order-ideal lat (conj #{} (first decomp-pair))) + set2 (order-ideal lat (conj #{} (last decomp-pair))) + order (lattice-order lat)] -(def ctx2 (make-context #{1 2 3 4 5} - #{"A" "B" "C" "D" "E"} - #{[1 "A"] [2 "A"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) -(def lat2 (concept-lattice ctx)) + [(make-lattice-nc set1 + order + (inf lat) + (sup lat)) + (make-lattice-nc set2 + order + (inf lat) + (sup lat))])) -(def ctx3 (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] - [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] - [7 "A"] [7 "B"] [7 "C"]})) -(def lat3 (concept-lattice ctx3)) From af727d12470f64583dc76baad3952e2ce0d3cb85 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 21 Sep 2023 19:07:57 +0200 Subject: [PATCH 071/117] Finished Documentation on Libkin Decomposition. --- doc/LibkinDecomposition.org | 617 +---------------------------- doc/images/cube-lattice.png | Bin 0 -> 68659 bytes doc/images/decomposed-lattice1.png | Bin 0 -> 39343 bytes doc/images/decomposed-lattice2.png | Bin 0 -> 44521 bytes 4 files changed, 16 insertions(+), 601 deletions(-) create mode 100644 doc/images/cube-lattice.png create mode 100644 doc/images/decomposed-lattice1.png create mode 100644 doc/images/decomposed-lattice2.png diff --git a/doc/LibkinDecomposition.org b/doc/LibkinDecomposition.org index e3a0e9067..8c6df8ca5 100644 --- a/doc/LibkinDecomposition.org +++ b/doc/LibkinDecomposition.org @@ -15,618 +15,33 @@ We will consider the following lattice as an example: (def lat (concept-lattice ctx)) #+end_src -** Creating Formal Contexts +[[./images/cube-lattice.png]] -~conexp-clj~ lets you easily create formal contexts in a number of ways. We -shall describe some of them in the following. - -A context ~(G,M,I)~ consists of two sets G and M and an incidence realtion I ⊆ -G×M. G is a set of /objects/, M is a set of /attributes/ and ~gIm~ (short for -(g,m) ∈ I) can be read as /g has the attribute m/. To create a context you only -have to define these sets. There a (at least) three options: - -*** Using a defined relation - -The fasted way to construct a formal context is just by writing it down, as in the following example. - -#+begin_src clojure :results silent -(def ctx-1 (make-context [1 2 3] [1 2 3] <=)) -#+end_src - -To see the formal context, just evaluate its variable explicitly +All decomposition pairs of the lattice can be computed using the method ~libkin-decomposition-pairs~: #+begin_src clojure :exports both -ctx-1 +(def pairs (libkin-decomposition-pairs lat)) #+end_src #+RESULTS: #+begin_src text - |1 2 3 ---+------ -1 |x x x -2 |. x x -3 |. . x - -#+end_src - -*** Defining all sets explicitly - -A formal context can also be specified by directly listing the incidence -relation (using Clojure's own syntax for sets and tuples): - -#+begin_src clojure :exports both -(def ctx-2 (make-context #{1 2 3 4 5 6} - #{1 2 3 4 5 6} - #{[1 1] [1 2] [1 3] [1 5] - [1 6] [2 2] [2 5] [3 3] - [3 6] [4 4] [4 5] [4 6] - [5 5] [6 6]})) -ctx-2 +([[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]] + [[#{7 4 2 5} #{"B"}] [#{7 6} #{"C" "A"}]] + [[#{7 1 4 6} #{"A"}] [#{7 5} #{"C" "B"}]] + [[#{7 5} #{"C" "B"}] [#{7 1 4 6} #{"A"}]] + [[#{7 6 3 5} #{"C"}] [#{7 4} #{"B" "A"}]] + [[#{7 1 4 6 3 2 5} #{}] [#{7} #{"C" "B" "A"}]] + [[#{7} #{"C" "B" "A"}] [#{7 1 4 6 3 2 5} #{}]] + [[#{7 4} #{"B" "A"}] [#{7 6 3 5} #{"C"}]]) #+end_src -#+RESULTS: -#+begin_src text - |1 2 3 4 5 6 ---+------------ -1 |x x x . x x -2 |. x . . x . -3 |. . x . . x -4 |. . . x x x -5 |. . . . x . -6 |. . . . . x - -#+end_src - -One can enter the cross-table explicitly, using the function -~make-context-from-matrix~, like this +The lattices implied by the decomposition through a specific decomposition pair can be exlicitely generated using ~libkin-decomposition-lattices~: #+begin_src clojure :exports both -(def ctx-3 (make-context-from-matrix 6 6 - [1 1 1 0 1 1 - 0 1 0 0 1 0 - 0 0 1 0 0 1 - 0 0 0 1 1 1 - 0 0 0 0 1 0 - 0 0 0 0 0 1])) -ctx-3 +(libkin-decomposition-lattices lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) #+end_src -#+RESULTS: -#+begin_src text - |0 1 2 3 4 5 ---+------------ -0 |x x x . x x -1 |. x . . x . -2 |. . x . . x -3 |. . . x x x -4 |. . . . x . -5 |. . . . . x - -#+end_src - -Here, instead of writing out the sets of objects and attributes explicitly, we -have just entered their cardinality ~6~. With this, the set of objects and -attributes automatically gets set to ~#{1 2 3 4 5 6}~. From time to time, this -make save some typing time. - -### Using a custom function - -This will create a formal context with G = M = {1,2,3,4,5,6} and (n,m) in I if -and only if gcd(n,m) = 1: - -#+begin_src clojure :exports both -(def ctx-4 (make-context [1 2 3 4 5 6] - [1 2 3 4 5 6] - (fn [x y] - (= 1 (gcd x y))))) -ctx-4 -#+end_src - -#+RESULTS: -#+begin_src text - |1 2 3 4 5 6 ---+------------ -1 |x x x x x x -2 |x . x . x . -3 |x x . x x . -4 |x . x . x . -5 |x x x x . x -6 |x . . . x . - -#+end_src - - -*** Creating Random Contexts - -For some experiments it is often helpful to randomly create contexts. Here is -how this can be done in conexp-clj. Of course, the exact result is probably not -the one you see here - -#+begin_src clojure :exports both -(rand-context #{1 2 3} 0.5) -#+end_src - -#+RESULTS: -#+begin_src text - |1 2 3 ---+------ -1 |x x x -2 |x x . -3 |x . x - -#+end_src - -Here, the first parameter is the set of objects and attributes and the second -parameter is the probality for the incidence. - -** Working with Formal Contexts - -Having created a formal context, there a plenty of possibilities to work with -it. - -*** Basic Accessors - -The most basic operation on formal contexts is to retrieve its components. This -can be done as follows - -#+begin_src clojure :exports both -[(objects ctx-2), (attributes ctx-2), (incidence ctx-2)] -#+end_src - -#+RESULTS: -#+begin_src text -[#{1 4 6 3 2 5} - #{1 4 6 3 2 5} - #{[2 2] [2 5] [3 3] [1 1] [6 6] [4 6] [1 3] [1 5] [5 5] [3 6] [4 5] - [1 6] [4 4] [1 2]}] -#+end_src - -*** Clarifying and Reducing Contexts - -To see if ~ctx-2~ is clarified, you can use the functions ~object-clarified?~, -~attribute-clarified?~, and ~context-clarified?~. - -#+begin_src clojure :exports both -[(object-clarified? ctx-2), - (attribute-clarified? ctx-2), - (context-clarified? ctx-2)] -#+end_src - -#+RESULTS: -#+begin_src text -[true true true] -#+end_src - -If ~ctx-2~ would not be clarified, one could obtain a clarified version of it by -using - -#+begin_src clojure :eval never :exports code -(clarify-attributes ctx-2) -(clarify-objects ctx-2) -(clarify-context ctx-2) -#+end_src - -As another example, for ~ctx-2~, we could for instance compute the arrow -relations (e.g. to see which objects or attributes are irreducible) - -#+begin_src clojure :exports both -[(up-arrows ctx-2), (down-arrows ctx-2)] -#+end_src - -#+RESULTS: -#+begin_src text -[#{[4 3] [6 3] [4 2] [6 5] [5 2] [1 4] [5 6] [2 6] [3 5]} - #{[4 3] [2 3] [4 2] [4 1] [1 4] [3 1] [2 1] [2 6] [3 5] [3 2]}] -#+end_src - -To directly see whether ~ctx-2~ is reduced, use ~context-reduced?~, and to -obtain a reduced version of ~ctx-2~, call ~reduce-context~ like so: - -#+begin_src clojure :exports both -(reduce-context ctx-2) -#+end_src - -#+RESULTS: -#+begin_src text - |2 3 4 5 6 ---+---------- -1 |x x . x x -2 |x . . x . -3 |. x . . x -4 |. . x x x - -#+end_src - -*** Derivation Operations - -Now I want to get all objects, which attribute ~1~ and ~2~ have in common - -#+begin_src clojure :exports both -(attribute-derivation ctx-2 #{1 2}) -#+end_src - -#+RESULTS: -#+begin_src text -#{1} -#+end_src - -The same can be done for sets of objects - -#+begin_src clojure :exports both -(object-derivation ctx-1 #{1 2}) -#+end_src - -#+RESULTS: -#+begin_src text -#{3 2} -#+end_src - -Instead of using this long function names, there are also the abbreviations -~aprime~ and ~oprime~ available. - -If you want to compute the closure of a given set of objects or attributes in -our context use - -#+begin_src clojure :exports both -[ (context-attribute-closure ctx-2 #{1 2}), - (context-object-closure ctx-2 #{1 2}) ] -#+end_src - -#+RESULTS: -#+begin_src text -[#{1 6 3 2 5} #{1 2}] -#+end_src - -*** Formal Concepts and Concept Lattices - -We can compute all intents and extents via - -#+begin_src clojure :exports both -[(extents ctx-2), (intents ctx-2)] -#+end_src - -#+RESULTS: -#+begin_src text -[(#{} - #{4} - #{1} - #{1 4} - #{1 2} - #{1 3} - #{1 4 2 5} - #{1 4 6 3} - #{1 4 6 3 2 5}) - (#{} - #{5} - #{2 5} - #{6} - #{6 5} - #{6 3} - #{4 6 5} - #{1 6 3 2 5} - #{1 4 6 3 2 5})] -#+end_src - -To get all formal concepts use - -#+begin_src clojure :exports both -(concepts ctx-2) -#+end_src - -#+RESULTS: -#+begin_src text -([#{1 4 6 3 2 5} #{}] - [#{1} #{1 6 3 2 5}] - [#{} #{1 4 6 3 2 5}] - [#{4} #{4 6 5}] - [#{1 4 6 3} #{6}] - [#{1 3} #{6 3}] - [#{1 4} #{6 5}] - [#{1 2} #{2 5}] - [#{1 4 2 5} #{5}]) -#+end_src - -If you are only interested in the number of formal concepts, you can instead -just ~count~ the concepts, like so - -#+begin_src clojure :exports both -(count (concepts ctx-2)) -#+end_src - -#+RESULTS: -#+begin_src text -9 -#+end_src - -This can be combined neatly with ~map~ to get the number of concepts for all the -formal contexts we have defined to far - -#+begin_src clojure :exports both -(map (comp count concepts) [ctx-1 ctx-2 ctx-3 ctx-4]) -#+end_src +[[./images/decomposed-lattice1.png]] +[[./images/decomposed-lattice2.png]] -#+RESULTS: -#+begin_src text -(3 9 9 8) -#+end_src - -The standard ~comp~ functions implements function composition in Clojure. - -Finally, you can compute the concept lattice using the ~concept-lattice~ -function like so: - -#+begin_src clojure :exports both -(concept-lattice ctx-2) -#+end_src - -#+RESULTS: -#+begin_src text -Lattice on 9 elements. -#+end_src - -Note that this will not give you a picture of the lattice, but a representation -of the algebraic structure. - -*** Canonical Base - -You get the canonical base with (who would have guessed that!) - -user=> (canonical-base ctx-1) -#{(#{b} ==> #{e}) (#{c} ==> #{f}) (#{c f e} ==> #{a b}) - (#{a} ==> #{c b f e}) (#{d} ==> #{f e}) (#{b f e} ==> #{a c})} - -The ~canonical-base~ function can take additional arguments like background -knowledge and filter predicates. See the documentation of this function for -further details: - -#+begin_src clojure :exports both -(doc canonical-base) -#+end_src - -#+RESULTS: -#+begin_src text -------------------------- -conexp.fca.implications/canonical-base -([ctx] [ctx background-knowledge] [ctx background-knowledge predicate]) - Returns the canonical base of given context, as a lazy sequence. Uses - «background-knowledge» as starting set of implications, which will not appear - in the result. If «predicate» is given (a function), computes only those - implications from the canonical base whose premise satisfy this predicate, - i.e. «predicate» returns true on these premises. Note that «predicate» has to - satisfy the same conditions as the predicate to «next-closed-set-in-family». -nil -#+end_src - -*** Further Operations - -There a several further operations you can do with contexts, e.g., the context -apposition, context subposition, and more. For illustration, let us define two -contexts: - -#+begin_src clojure :exports both -(def ctx-5 (make-context #{1 2 3} #{1 2 3} <)) -(def ctx-6 (make-context-from-matrix [1 2 3] - ['a 'b 'c 'd] - [1 1 0 1 - 1 0 1 0 - 0 0 1 1])) -[ctx-5 ctx-6] -#+end_src - -#+RESULTS: -#+begin_src text -[ |1 2 3 ---+------ -1 |. x x -2 |. . x -3 |. . . - |a b c d ---+-------- -1 |x x . x -2 |x . x . -3 |. . x x -] -#+end_src - -The apposition of these two contexts is - -#+begin_src clojure :exports both -(context-apposition ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |[1 0] [2 0] [3 0] [a 1] [b 1] [c 1] [d 1] ---+------------------------------------------ -1 |. x x x x . x -2 |. . x x . x . -3 |. . . . . x x - -#+end_src - -Note how the two sets of attributes are automatically made disjoint by -considering pairs with different second entry. - -Context apposition is a partial operation, as the contexts must have the same -set of objects. The following would not work: - -#+begin_src clojure :exports both -(context-apposition ctx-1 ctx-2) -#+end_src - -#+RESULTS: -#+begin_src text -class java.lang.IllegalArgumentExceptionclass java.lang.IllegalArgumentExceptionIllegalArgumentException Cannot do context apposition, since object sets are not equal. conexp.base/illegal-argument (base.clj:280) -#+end_src - -To compute the dual context, use what you would expect to use: - -#+begin_src clojure :exports both -(dual-context ctx-5) -#+end_src - -#+RESULTS: -#+begin_src text - |1 2 3 ---+------ -1 |. . . -2 |x . . -3 |x x . - -#+end_src - -Now we can build the subposition of ~ctx-5~ and the dual of ~ctx-6~ - -#+begin_src clojure :exports both -(context-subposition ctx-5 (dual-context ctx-6)) -#+end_src - -#+RESULTS: -#+begin_src text - |1 2 3 -------+------ -[1 0] |. x x -[2 0] |. . x -[3 0] |. . . -[a 1] |x x . -[b 1] |x . . -[c 1] |. x x -[d 1] |x . x - -#+end_src - -If you want to invert a given context use - -#+begin_src clojure :exports both -(invert-context ctx-5) -#+end_src - -#+RESULTS: -#+begin_src text - |1 2 3 ---+------ -1 |x . . -2 |x x . -3 |x x x - -#+end_src - -You can create a composition of two (suitable) contexts with - -#+begin_src clojure :exports both -(context-composition ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |a b c d ---+-------- -1 |x . x x -2 |. . x x -3 |. . . . - -#+end_src - -The union of two contexts is created by - -#+begin_src clojure :exports both -(context-union ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |a b c d 1 2 3 ---+-------------- -1 |x x . x . x x -2 |x . x . . . x -3 |. . x x . . . - -#+end_src - -Sum to contexts with - -#+begin_src clojure :exports both -(context-sum ctx-5 ctx-6) -#+end_src - -To compute the intersection of two contexts (which is essentially empty), use - -#+begin_src clojure :exports both -(context-intersection ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - | ---+ -1 | -2 | -3 | - -#+end_src - -The context product goes like this - -#+begin_src clojure :exports both -(context-product ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |[1 a] [2 a] [3 a] [1 b] [2 b] [3 b] [1 c] [2 c] [3 c] [1 d] [2 d] [3 d] -------+------------------------------------------------------------------------ -[1 1] |x x x x x x . x x x x x -[2 1] |x x x x x x . . x x x x -[3 1] |x x x x x x . . . x x x -[1 2] |x x x . x x x x x . x x -[2 2] |x x x . . x x x x . . x -[3 2] |x x x . . . x x x . . . -[1 3] |. x x . x x x x x x x x -[2 3] |. . x . . x x x x x x x -[3 3] |. . . . . . x x x x x x - -#+end_src - -If you want to do a context semiproduct - -#+begin_src clojure :exports both -(context-semiproduct ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |[1 0] [2 0] [3 0] [a 1] [b 1] [c 1] [d 1] -------+------------------------------------------ -[1 1] |. x x x x . x -[2 1] |. . x x x . x -[3 1] |. . . x x . x -[1 2] |. x x x . x . -[2 2] |. . x x . x . -[3 2] |. . . x . x . -[1 3] |. x x . . x x -[2 3] |. . x . . x x -[3 3] |. . . . . x x - -#+end_src - -Compute Xia's product - -#+begin_src clojure :exports both -(context-xia-product ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |[1 a] [2 a] [3 a] [1 b] [2 b] [3 b] [1 c] [2 c] [3 c] [1 d] [2 d] [3 d] -------+------------------------------------------------------------------------ -[1 1] |. x x . x x x . . . x x -[2 1] |. . x . . x x x . . . x -[3 1] |. . . . . . x x x . . . -[1 2] |. x x x . . . x x x . . -[2 2] |. . x x x . . . x x x . -[3 2] |. . . x x x . . . x x x -[1 3] |x . . x . . . x x . x x -[2 3] |x x . x x . . . x . . x -[3 3] |x x x x x x . . . . . . - -#+end_src +These lattices may be visualized as described in Concept-Lattices.org . \ No newline at end of file diff --git a/doc/images/cube-lattice.png b/doc/images/cube-lattice.png new file mode 100644 index 0000000000000000000000000000000000000000..7c2ceaab5f064656423944cabe7c80c5144571c2 GIT binary patch literal 68659 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zgU1D%+9K2BrSWTFNhJiRQ*lHLe`S@&^?!@OfOrhC23>F)#8JX34iB!S;j|Qr2U+S(CRQz}a3x w-^rzkOT-;wSlu5#sAP=lyr=MDI4V_l2j$=6U;WsCTDQBlJ8#SR&g Date: Thu, 21 Sep 2023 20:38:58 +0200 Subject: [PATCH 072/117] Added Test for Libkin Decomposition. --- .../clojure/conexp/fca/decompositions.clj | 2 +- .../conexp/fca/decompositions_test.clj | 46 +++++++++++++++++++ 2 files changed, 47 insertions(+), 1 deletion(-) create mode 100644 src/test/clojure/conexp/fca/decompositions_test.clj diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index 73c84c740..fca353a1b 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -25,7 +25,7 @@ (defn libkin-decomposition-lattices "Computes the Lattices Resulting from the Libkin-Decomposition on the - Providen Decomposition Pair." + Provided Decomposition Pair." [lat decomp-pair] (let [set1 (order-ideal lat (conj #{} (first decomp-pair))) set2 (order-ideal lat (conj #{} (last decomp-pair))) diff --git a/src/test/clojure/conexp/fca/decompositions_test.clj b/src/test/clojure/conexp/fca/decompositions_test.clj new file mode 100644 index 000000000..822489e9b --- /dev/null +++ b/src/test/clojure/conexp/fca/decompositions_test.clj @@ -0,0 +1,46 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.decompositions-test + (:require [conexp.base :refer :all] + [conexp.math.algebra :refer :all] + [conexp.fca + [contexts :refer :all] + [metrics :refer :all] + [lattices :refer :all] + [posets :refer :all] + [decompositions :refer :all]]) + (:use clojure.test)) + + +(deftest test-libkin + (let [ctx (make-context #{1 2 3 4 5 6 7} + #{"A" "B" "C"} + #{[1 "A"] [2 "B"] [3 "C"] + [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] + [7 "A"] [7 "B"] [7 "C"]}) + cube-lat (concept-lattice ctx) + cube-lat-decomp-pairs (seq [[[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]] + [[#{7 4 2 5} #{"B"}] [#{7 6} #{"C" "A"}]] + [[#{7 1 4 6} #{"A"}] [#{7 5} #{"C" "B"}]] + [[#{7 5} #{"C" "B"}] [#{7 1 4 6} #{"A"}]] + [[#{7 6 3 5} #{"C"}] [#{7 4} #{"B" "A"}]] + [[#{7 1 4 6 3 2 5} #{}] [#{7} #{"C" "B" "A"}]] + [[#{7} #{"C" "B" "A"}] [#{7 1 4 6 3 2 5} #{}]] + [[#{7 4} #{"B" "A"}] [#{7 6 3 5} #{"C"}]]]) + decomp-ctx1 (make-context #{6 7} + #{"A" "B" "C"} + #{[6 "A"] [6 "C"] [7 "A"] [7 "B"] [7 "C"]}) + decomp-lat1 (concept-lattice decomp-ctx1) + decomp-ctx2 (make-context #{2 4 5 7} + #{"A" "B" "C"} + #{[2 "B"] [4 "A"] [4 "B"] [5 "B"] [5 "C"] [7 "A"] [7 "B"] [7 "C"]}) + decomp-lat2 (concept-lattice decomp-ctx2)] + + (is (= (libkin-decomposition-pairs cube-lat) cube-lat-decomp-pairs)) + (is (= (libkin-decomposition-lattices cube-lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) [decomp-lat1 decomp-lat2])))) From 307294a97fc84e93a52cb2c5f62449608af194bb Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Tue, 26 Sep 2023 22:08:06 +0200 Subject: [PATCH 073/117] Implemented Poset Product. --- src/main/clojure/conexp/fca/posets.clj | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/src/main/clojure/conexp/fca/posets.clj b/src/main/clojure/conexp/fca/posets.clj index c93be4897..026da28ee 100644 --- a/src/main/clojure/conexp/fca/posets.clj +++ b/src/main/clojure/conexp/fca/posets.clj @@ -9,7 +9,8 @@ (ns conexp.fca.posets (:require [conexp.base :refer :all] [conexp.math.algebra :refer :all] - [conexp.fca.contexts :refer :all])) + [conexp.fca.contexts :refer :all] + [clojure.math.combinatorics :refer [cartesian-product]])) (deftype Poset [base-set order-function] Object @@ -161,3 +162,10 @@ (recur (union filter #{next-element}) (union upper-neighbours (poset-upper-neighbours poset next-element)) (first (difference upper-neighbours filter)))))) + +(defn poset-product + [a b] + (make-poset (cartesian-product (base-set a) (base-set b)) + (fn [x y] (and ((order a) (first x) (first y)) + ((order b) (last x) (last y))))) +) From ad157e0ea118f0b34f118e0adbbcca476149735c Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 27 Sep 2023 17:13:39 +0200 Subject: [PATCH 074/117] Implemented Product Functions for Posets and Lattices. Improved Tests and Documentation. --- doc/LibkinDecomposition.org | 11 ++- doc/images/cube-lattice.png | Bin 68659 -> 79656 bytes doc/images/decomposed-lattice1.png | Bin 39343 -> 43363 bytes doc/images/decomposed-lattice2.png | Bin 44521 -> 47096 bytes doc/images/prod-lattice.png | Bin 0 -> 96875 bytes src/main/clojure/conexp/fca/lattices.clj | 9 ++- .../conexp/fca/decompositions_test.clj | 68 +++++++++++++----- 7 files changed, 68 insertions(+), 20 deletions(-) create mode 100644 doc/images/prod-lattice.png diff --git a/doc/LibkinDecomposition.org b/doc/LibkinDecomposition.org index 8c6df8ca5..b72bc1df5 100644 --- a/doc/LibkinDecomposition.org +++ b/doc/LibkinDecomposition.org @@ -17,6 +17,9 @@ We will consider the following lattice as an example: [[./images/cube-lattice.png]] +A Libkin decomposition of a lattice L is a pair of sublattices of L, whose product is isomorphic to L. +Libkin decompositions are each induced by a decomposition pair, a neutral element in L and its Complement. + All decomposition pairs of the lattice can be computed using the method ~libkin-decomposition-pairs~: #+begin_src clojure :exports both @@ -35,13 +38,19 @@ All decomposition pairs of the lattice can be computed using the method ~libkin- [[#{7 4} #{"B" "A"}] [#{7 6 3 5} #{"C"}]]) #+end_src +Computing the order ideal of both entries of the pair yields the two sublattices forming the decomposition. + The lattices implied by the decomposition through a specific decomposition pair can be exlicitely generated using ~libkin-decomposition-lattices~: #+begin_src clojure :exports both (libkin-decomposition-lattices lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) #+end_src +These lattices may be visualized as described in Concept-Lattices.org . + [[./images/decomposed-lattice1.png]] [[./images/decomposed-lattice2.png]] -These lattices may be visualized as described in Concept-Lattices.org . \ No newline at end of file +The product of these lattices yields a lattice isomorphic to L: + 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Datastructure @@ -460,6 +461,12 @@ (let [B+D (intersection B D)] [(attribute-derivation ctx B+D) B+D])))))) +(defn lattice-product + [a b] + (make-lattice (cartesian-product (base-set a) (base-set b)) + (fn [x y] (and ((order a) (first x) (first y)) + ((order b) (last x) (last y)))))) + ;;; nil diff --git a/src/test/clojure/conexp/fca/decompositions_test.clj b/src/test/clojure/conexp/fca/decompositions_test.clj index 822489e9b..19f8900df 100644 --- a/src/test/clojure/conexp/fca/decompositions_test.clj +++ b/src/test/clojure/conexp/fca/decompositions_test.clj @@ -17,30 +17,62 @@ [decompositions :refer :all]]) (:use clojure.test)) - -(deftest test-libkin - (let [ctx (make-context #{1 2 3 4 5 6 7} +;cube context +(def ctx1 (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] - [7 "A"] [7 "B"] [7 "C"]}) - cube-lat (concept-lattice ctx) - cube-lat-decomp-pairs (seq [[[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]] + [7 "A"] [7 "B"] [7 "C"]})) +(def lat1 (concept-lattice ctx1)) + +(def decomp-pairs1 (seq [[[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]] [[#{7 4 2 5} #{"B"}] [#{7 6} #{"C" "A"}]] [[#{7 1 4 6} #{"A"}] [#{7 5} #{"C" "B"}]] [[#{7 5} #{"C" "B"}] [#{7 1 4 6} #{"A"}]] [[#{7 6 3 5} #{"C"}] [#{7 4} #{"B" "A"}]] [[#{7 1 4 6 3 2 5} #{}] [#{7} #{"C" "B" "A"}]] [[#{7} #{"C" "B" "A"}] [#{7 1 4 6 3 2 5} #{}]] - [[#{7 4} #{"B" "A"}] [#{7 6 3 5} #{"C"}]]]) - decomp-ctx1 (make-context #{6 7} - #{"A" "B" "C"} - #{[6 "A"] [6 "C"] [7 "A"] [7 "B"] [7 "C"]}) - decomp-lat1 (concept-lattice decomp-ctx1) - decomp-ctx2 (make-context #{2 4 5 7} - #{"A" "B" "C"} - #{[2 "B"] [4 "A"] [4 "B"] [5 "B"] [5 "C"] [7 "A"] [7 "B"] [7 "C"]}) - decomp-lat2 (concept-lattice decomp-ctx2)] - - (is (= (libkin-decomposition-pairs cube-lat) cube-lat-decomp-pairs)) - (is (= (libkin-decomposition-lattices cube-lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) [decomp-lat1 decomp-lat2])))) + [[#{7 4} #{"B" "A"}] [#{7 6 3 5} #{"C"}]]])) +(def ctx1-decomp-1 (concept-lattice (make-context #{6 7} + #{"A" "B" "C"} + #{[6 "A"] [6 "C"] [7 "A"] [7 "B"] [7 "C"]}))) +(def ctx1-decomp-2 (concept-lattice (make-context #{2 4 5 7} + #{"A" "B" "C"} + #{[2 "B"] [4 "A"] [4 "B"] [5 "B"] [5 "C"] [7 "A"] [7 "B"] [7 "C"]}))) + +;no libkin decompositions +(def ctx2 (make-context #{1 2 3 4 5} + #{1 2 3 4 5} + #{[1 2] [1 3] [1 5] + [2 3] + [3 1] [3 2] [3 3] [3 4] + [4 3] [4 4] + [5 3] [5 5]})) +(def lat2 (concept-lattice ctx2)) + +;only decomposable by top and bot +(def ctx3 (make-context #{1 2 3 4 5 6} + #{1 2 3 4 5 6} + #{[1 1] [1 4] [1 5] + [2 1] [2 5] [2 6] + [3 2] [3 6] + [4 1] [4 5] + [5 2] [5 4] + [6 2] [6 3] [6 4] [6 5]})) +(def lat3 (concept-lattice ctx3)) +(def decomp-pairs3 (seq [[[#{} #{1 4 6 3 2 5}] [#{1 4 6 3 2 5} #{}]] + [[#{1 4 6 3 2 5} #{}] [#{} #{1 4 6 3 2 5}]]])) + + +(deftest test-libkin + + (is (= (libkin-decomposition-pairs lat1) + decomp-pairs1)) + (is (= (libkin-decomposition-lattices lat1 [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) + [ctx1-decomp-1 ctx1-decomp-2])) + + (is (empty? (libkin-decomposition-pairs lat2))) + + (is (= (libkin-decomposition-pairs lat3) + decomp-pairs3)) +) From d123e7f8b9831847f6343fc205ce06dbe831d641 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 28 Sep 2023 16:57:56 +0200 Subject: [PATCH 075/117] Added Libkin Decomposition Documentation to Index. --- README.md | 1 + 1 file changed, 1 insertion(+) diff --git a/README.md b/README.md index f5925b81a..429ef1b7b 100644 --- a/README.md +++ b/README.md @@ -32,6 +32,7 @@ much more. 8. [Computing Traces in Contexts](doc/code/trace-context.clj) 9. [Counting Quasiorders](doc/code/quasiorders.clj) 10. [Rudolph's Algorithm for Computing Bases](doc/code/rudolph_computation.clj) + 11. [Libkin Decompositions](doc/LibkinDecomposition.org) 5. Advanced Topics 1. [pq-cores](doc/pq-cores-in-Formal-Contexts.md) 2. [REST-API Usage](doc/REST-API-usage.md) From 7618e671b7176e196b36bfa224f7881f92e41caa Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 4 Oct 2023 20:09:31 +0200 Subject: [PATCH 076/117] Improved Documentation. --- doc/LibkinDecomposition.org | 9 +++++++-- doc/images/car-lattice.png | Bin 0 -> 531171 bytes doc/images/decomposed-lattice1.png | Bin 43363 -> 217120 bytes doc/images/decomposed-lattice2.png | Bin 47096 -> 101493 bytes 4 files changed, 7 insertions(+), 2 deletions(-) create mode 100644 doc/images/car-lattice.png diff --git a/doc/LibkinDecomposition.org b/doc/LibkinDecomposition.org index b72bc1df5..a361d21cd 100644 --- a/doc/LibkinDecomposition.org +++ b/doc/LibkinDecomposition.org @@ -15,7 +15,7 @@ We will consider the following lattice as an example: (def lat (concept-lattice ctx)) #+end_src -[[./images/cube-lattice.png]] +[[./images/car-lattice.png]] A Libkin decomposition of a lattice L is a pair of sublattices of L, whose product is isomorphic to L. Libkin decompositions are each induced by a decomposition pair, a neutral element in L and its Complement. @@ -43,11 +43,16 @@ Computing the order ideal of both entries of the pair yields the two sublattices The lattices implied by the decomposition through a specific decomposition pair can be exlicitely generated using ~libkin-decomposition-lattices~: #+begin_src clojure :exports both -(libkin-decomposition-lattices lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) +(def lattice-pair (libkin-decomposition-lattices lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]])) #+end_src These lattices may be visualized as described in Concept-Lattices.org . +#+begin_src text +(draw-lattice (first lattice-pair)) +(draw-lattice (last lattice-pair)) +#+end_src + [[./images/decomposed-lattice1.png]] [[./images/decomposed-lattice2.png]] diff --git a/doc/images/car-lattice.png b/doc/images/car-lattice.png new file mode 100644 index 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z>v=icVkfd~4Wnk=g*|CRVzVOEB25jaszl2$2sx;#$*72E^v7SE3UDxRKl09OPL=HN zf6H`LQDg@9W#id1*`k*{^*vtHSCT23$xkg9?jF36lw-S*k~R?wLVE(B8x;Z+h%zgH015bhGKgd;JH4G?csJw~7ww3S8h;52#>o#cf za8p*K8~KqmlK`8S*a~)yLe{-bFH>A)bo-NkP*iylFVBRMQLHxFV9{1@segzQ>@TRX zIvaANJ08~>Im%6R{u+0U5E=t}3KyhP%~4)j!w| zr~?7r`&MrHXCvvu|q?sJNI!0o%GH8IxG4b z87E+-4k!>aMjj68{?)FTL+zQ#+4Yusv|5x+?qF2RFzRM3H>Qc=-%@w=_~p6PPAb=o zw-{~mKf+&0J@~w;KmV%1begbs$kAED;sJ$sv?!%jEj8}zv)@xm4nb9#IyKT*DipB+3^K~MhggzMmB;2Rc_VckJw~>&S^!Immn__FI;d!IB<^sWi v+=CqFJ&E-CHVPk)p>FoygJX<|7WQiW`tjm<-eL3%eC&wnPpSX0`}O|=ITuoV From 709ff015fd0ee4bca4b1476a4ef2827fbe39be39 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Sat, 28 Oct 2023 20:08:27 +0200 Subject: [PATCH 077/117] Fixed Imlementation of Complement Computation. --- src/main/clojure/conexp/fca/metrics.clj | 19 +++++++++++-------- .../conexp/fca/decompositions_test.clj | 6 +++++- 2 files changed, 16 insertions(+), 9 deletions(-) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 48de93a31..03192e6ab 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -837,23 +837,26 @@ ) ) +(defn top-element [lat] + (reduce #((sup lat) %1 %2) (lattice-base-set lat)) +) + +(defn bot-element [lat] + (reduce #((inf lat) %1 %2) (lattice-base-set lat)) +) + ;retruns all complements of "concept" in "lat" (defn element-complement [concept lat] - (let [base-set (lattice-base-set lat) - top (first(filter #(= (second %) #{}) base-set)) - bot (reduce #(if (> (count (second %1)) (count (second %2))) %1 - %2 - ) base-set)] + (let [base-set (lattice-base-set lat)] (filter #(and (not= % concept) - (= ((sup lat) concept %) top) - (= ((inf lat) concept %) bot)) + (= ((sup lat) concept %) (top-element lat)) + (= ((inf lat) concept %) (bot-element lat))) base-set)) ) - ;;; nil diff --git a/src/test/clojure/conexp/fca/decompositions_test.clj b/src/test/clojure/conexp/fca/decompositions_test.clj index 19f8900df..ff5cd7e84 100644 --- a/src/test/clojure/conexp/fca/decompositions_test.clj +++ b/src/test/clojure/conexp/fca/decompositions_test.clj @@ -50,6 +50,9 @@ [5 3] [5 5]})) (def lat2 (concept-lattice ctx2)) +(def decomp-pairs-2 (seq [[[#{1 4 3 2 5} #{3}] [#{} #{1 4 3 2 5}]] + [[#{} #{1 4 3 2 5}] [#{1 4 3 2 5} #{3}]]])) + ;only decomposable by top and bot (def ctx3 (make-context #{1 2 3 4 5 6} #{1 2 3 4 5 6} @@ -71,7 +74,8 @@ (is (= (libkin-decomposition-lattices lat1 [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) [ctx1-decomp-1 ctx1-decomp-2])) - (is (empty? 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From c46ce67c9e4670b0a0bb81a5488b8c9fc87ec708 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 2 Nov 2023 22:01:49 +0100 Subject: [PATCH 079/117] Removed Redundant Functions. --- src/main/clojure/conexp/fca/metrics.clj | 18 +++++------------- 1 file changed, 5 insertions(+), 13 deletions(-) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 03192e6ab..a47b8fcb8 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -35,7 +35,9 @@ make-lattice-nc concept-lattice lattice-order - distributive?]]] + distributive? + lattice-one + lattice-zero]]] [conexp.math.util :refer [eval-polynomial binomial-coefficient]]) (:import [conexp.fca.lattices Lattice] [java.util ArrayList BitSet])) @@ -837,26 +839,16 @@ ) ) -(defn top-element [lat] - (reduce #((sup lat) %1 %2) (lattice-base-set lat)) -) - -(defn bot-element [lat] - (reduce #((inf lat) %1 %2) (lattice-base-set lat)) -) ;retruns all complements of "concept" in "lat" (defn element-complement [concept lat] (let [base-set (lattice-base-set lat)] (filter #(and (not= % concept) - (= ((sup lat) concept %) (top-element lat)) - (= ((inf lat) concept %) (bot-element lat))) + (= ((sup lat) concept %) (lattice-one lat)) + (= ((inf lat) concept %) (lattice-zero lat))) base-set)) ) - - - ;;; nil From bd43ec50ded9da829930ae031e0b11cc356a2f4a Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Fri, 3 Nov 2023 00:32:10 +0100 Subject: [PATCH 080/117] Added Decompositions Namespace to Documentation. --- doc/LibkinDecomposition.org | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/doc/LibkinDecomposition.org b/doc/LibkinDecomposition.org index a361d21cd..9c78994b1 100644 --- a/doc/LibkinDecomposition.org +++ b/doc/LibkinDecomposition.org @@ -6,6 +6,15 @@ ~conexp-clj~ allows for the computation of Libkin Decompositions of lattices. For an explanation of the concept consult "Direct product decompositions of lattices, closures and relation schemes" by Leonid Libkin +Some of the following functions require the ~decompositions~ namespace: + + +#+begin_src clojure +(use 'conexp.fca.decompositions) +#+end_src + +(use 'conexp.fca.decompositions) + We will consider the following lattice as an example: #+begin_src clojure :exports both From 8a0b5259fac76958aa968f856cdf0c662ed6a5b2 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Sun, 26 Nov 2023 17:15:10 +0100 Subject: [PATCH 081/117] Implemented Distributive Exploration Algorithm. --- birddiet-d.ctx | 29 + .../clojure/conexp/fca/decompositions.clj | 51 +- testing-data/alle_taschenmesser.csv | 161 + testing-data/california.ctx | 51 + testing-data/gewuerzplaner.cxt | 154 + testing-data/lattice.txt | 2 + testing-data/mushroom.ctx | 16372 ++++++++++++++++ testing-data/zoo.ctx | 250 + 8 files changed, 17069 insertions(+), 1 deletion(-) create mode 100644 birddiet-d.ctx create mode 100644 testing-data/alle_taschenmesser.csv create mode 100644 testing-data/california.ctx create mode 100644 testing-data/gewuerzplaner.cxt create mode 100644 testing-data/lattice.txt create mode 100644 testing-data/mushroom.ctx create mode 100644 testing-data/zoo.ctx diff --git a/birddiet-d.ctx b/birddiet-d.ctx new file mode 100644 index 000000000..cb621e0d6 --- /dev/null +++ b/birddiet-d.ctx @@ -0,0 +1,29 @@ +B + +10 +4 + +fink +baumläufer +zaunkönig +kleiber +dompfaff +amsel +wintergoldhähnchen +girlitz +sperling +meise +sonnenblume +beeren +haferflocken +äpfel +X... +..X. +.... +X... +XX.. +.XXX +.... +.... +X.X. +X... diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index fca353a1b..e5b49a574 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -6,9 +6,10 @@ ;; the terms of this license. ;; You must not remove this notice, or any other, from this software. -(ns conexp.fca.decompositions +#(ns conexp.fca.decompositions (:require [conexp.base :refer :all] [conexp.math.algebra :refer :all] + [conexp.io.contexts :refer :all] [conexp.fca [contexts :refer :all] [metrics :refer :all] @@ -41,3 +42,51 @@ (inf lat) (sup lat))])) +(defn add-obj [ctx obj incidence] + "Returns a new context with obj added." + (make-context (union (objects ctx) #{obj}) (attributes ctx) incidence)) + + +(defn add-attr [ctx attr incidence] + (make-context (objects ctx) (union (attributes ctx) #{attr}) incidence)) + + + +(defn distributive-exploration [ctx empty-ctx] + (let [objs (objects ctx) + attr (attributes ctx) + incidence (incidence ctx) + start empty-ctx] + + (loop [subctx start + rest-objs objs + rest-attr attr + object-next true] + + (let [new-obj (first (filter #(distributive? (concept-lattice (add-obj subctx % incidence))) rest-objs)) + new-attr (first (filter #(distributive? (concept-lattice (add-attr subctx % incidence))) rest-attr))] + + (if (not (or new-obj new-attr)) + subctx + (if (and object-next new-obj) + (recur (add-obj subctx new-obj incidence) + (difference rest-objs #{new-obj}) + rest-attr + false) + (if (and (not object-next) new-attr) + (recur (add-attr subctx new-attr incidence) + rest-objs + (difference rest-attr #{new-attr}) + true) + (recur subctx + rest-objs + rest-attr + (not object-next))))) + ) + ))) + + + + +;(def ctx (rad-context "testing-data/Bird-Diet.ctx")) +;(make-context #{} #{} (incidence ctx)) diff --git a/testing-data/alle_taschenmesser.csv b/testing-data/alle_taschenmesser.csv new file mode 100644 index 000000000..df5f998c9 --- /dev/null +++ b/testing-data/alle_taschenmesser.csv @@ -0,0 +1,161 @@ +,Drahtschaber,Muttergreifer,Phillips-Schraubendreher 0/1. lang,Massstab (inches),Befestigungsöse,USB Stick 3.0/3.1,grosse Klinge ohne Spitze,Drahtabisolierer,Metallfeile,Hakenklinge,Digital-Uhr (24h),Hufreiniger,Dosenöffner,Hülsenpresser,Schraubendreher 3.5 mm,Orangenschäler,Metallsäge,Zahnstocher,LED,Bit Hex 2.5,Käseklinge,Paracord-Anhänger,Marlspieker,Phillips-Schraubendreher 1/2,Innensechskant für D-SUB-Steckverbinder 5 mm,kleine Klinge,Wasserwaage,Thermometer (°C),Schraubendreher 6 mm,Bit Phillips 0 (Pozidrive),Schäkelöffner,Scheibenzertrümmerer,Bit Torx 8,zwei Öffnungspositionen,Bit Phillips 3,Bit-Halter,Bit Schlitz 3,Phillips-Schraubendreher 0/1. magnetisch,Nagelknipser,Drahtschneider,Bit Hex 2,Kapselschneider,Bit Hex 1.5,Korkenzieher,Bit Phillips 2,Visiervorrichtung,Spitzzange,kleine Waidklinge,Schere mit Mikrozahnung,Holzsäge,Timer,Mehrzweckhaken,Schraubendreher 5 mm,Thermometer (°F),Stech-Bohr-Nähahle,Barometer,Uhrengehäuseöffner,Abziehstein,Bit Hex 1.2,grosse Klinge,Bit Phillips 1 (Pozidrive),Bit-Schlüssel,Schraubendreher 3 mm,Pinzette,Bit Hex 4,Stecknadel. inox,Druckkugelschreiber,Nagelhautschieber,Holzmeissel 4 mm,Schere,Innensechskant 4 mm für Bits,Bit Torx 10,Fischentschupper,Bit Schlitz 4,Money Clip,Kombi-Zange,zweistufige Stütze,Schraubenzieher 2.5 mm,Lupe,Angellöser,grosse Klinge mit Damast-Stahl,Kapselheber,Massstab (cm),Nagelfeile,Clip,Bit Torx 6,Kabelklinge,Altimeter (Fuss),Gurtenschneider,Digital-Uhr (12h),Nagelreiniger,Kompass,Countdown,Gabelschlüssel M3. 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b/testing-data/california.ctx new file mode 100644 index 000000000..61c48b206 --- /dev/null +++ b/testing-data/california.ctx @@ -0,0 +1,51 @@ +B +National Parks in California +19 +8 + +Cabrillo Natl. Mon. +Channel Islands Natl. Park +Death Valley Natl. Mon +Devils Postpile Natl. Mon +Fort Point Natl. Historic Site +Golden Gate Natl. Recreation Area +John Muir Natl. Historic Site +Joshua Tree Natl. Mon. +Kings Canyon Natl. Park +Lassen Volcanic Natl. Park +Lava Beds Natl. Mon. +Muir Woods Natl. Mon. +Pinnacles Natl. Mon. +Point Reyes Natl. Seashore +Redwood Natl. Park +Santa Monica Mts. Natl. Recr. Area +Sequoia Natl. Park +Whiskeytown-Shasta-Trinity Natl. Recs. Area +Yosemite Natl. 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+...X.X..X.XXXX...XX.XX..X...X.XX....XX..... +X.X..X...X...X.X.X..XXX.X.XX.....X..XX.X... \ No newline at end of file From 9074412e8e964907d5c103493fa1432e22fb9f47 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Tue, 28 Nov 2023 00:19:27 +0100 Subject: [PATCH 082/117] Computed Distributive Sublattice. --- animals-d.ctx | 15 + birddiet-d.ctx => bird-diet-d.ctx | 0 bodiesofwater-d.ctx | 30 ++ booth-d.ctx | 128 +++++++ brunson-club-d.ctx | 36 ++ cointoss-2-d.ctx | 137 ++++++++ diagnosis-d.ctx | 132 +++++++ digits-d.ctx | 28 ++ dirichlet-1-d.ctx | 326 ++++++++++++++++++ dolphins-d.ctx | 87 +++++ drive_concepts_for_motorcars-d.ctx | 33 ++ forum-romanum-d.ctx | 27 ++ gewuerzplaner-d.ctx | 62 ++++ living-beings-and-water-d.ctx | 22 ++ myctx-d.ctx | 17 + olympic-disciplines-d.ctx | 66 ++++ seasoning-planner-d.ctx | 62 ++++ southern-woman-d.ctx | 39 +++ .../clojure/conexp/fca/decompositions.clj | 40 ++- testcontext-d.ctx | 14 + triangles-d.ctx | 21 ++ wood-properties-d.ctx | 45 +++ zoo-d.ctx | 134 +++++++ 23 files changed, 1496 insertions(+), 5 deletions(-) create mode 100644 animals-d.ctx rename birddiet-d.ctx => bird-diet-d.ctx (100%) create mode 100644 bodiesofwater-d.ctx create mode 100644 booth-d.ctx create mode 100644 brunson-club-d.ctx create mode 100644 cointoss-2-d.ctx create mode 100644 diagnosis-d.ctx create mode 100644 digits-d.ctx create mode 100644 dirichlet-1-d.ctx create mode 100644 dolphins-d.ctx create mode 100644 drive_concepts_for_motorcars-d.ctx create mode 100644 forum-romanum-d.ctx create mode 100644 gewuerzplaner-d.ctx create mode 100644 living-beings-and-water-d.ctx create mode 100644 myctx-d.ctx create mode 100644 olympic-disciplines-d.ctx create mode 100644 seasoning-planner-d.ctx create mode 100644 southern-woman-d.ctx create mode 100644 testcontext-d.ctx create mode 100644 triangles-d.ctx create mode 100644 wood-properties-d.ctx create mode 100644 zoo-d.ctx diff --git a/animals-d.ctx b/animals-d.ctx new file mode 100644 index 000000000..57ecc270a --- /dev/null +++ b/animals-d.ctx @@ -0,0 +1,15 @@ +B + +3 +4 + +bird +penguin +pidgeon +eggs +cannot fly +warm-blooded +can fly +X.X. +XXX. +X.XX diff --git a/birddiet-d.ctx b/bird-diet-d.ctx similarity index 100% rename from birddiet-d.ctx rename to bird-diet-d.ctx diff --git a/bodiesofwater-d.ctx b/bodiesofwater-d.ctx new file mode 100644 index 000000000..e416acad8 --- /dev/null +++ b/bodiesofwater-d.ctx @@ -0,0 +1,30 @@ +B + +10 +5 + +river +stream +reservoir +puddle +sea +lagoon +rivulet +runnel +trickle +torrent +running +maritime +constant +natural +stagnant +X.XX. +X.XX. +..X.X +...XX +.XXXX +.XXXX +X.XX. +X.XX. +X.XX. +X.XX. diff --git a/booth-d.ctx b/booth-d.ctx new file mode 100644 index 000000000..5e078b5a0 --- /dev/null +++ b/booth-d.ctx @@ -0,0 +1,128 @@ +B + +48 +27 + +Obj 41 +Obj 32 +Obj 47 +Obj 28 +Obj 1 +Obj 63 +Obj 40 +Obj 60 +Obj 5 +Obj 46 +Obj 53 +Obj 57 +Obj 2 +Obj 62 +Obj 39 +Obj 61 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b/brunson-club-d.ctx @@ -0,0 +1,36 @@ +B + +11 +9 + +U_17 +U_3 +U_4 +U_10 +U_24 +U_14 +U_11 +U_22 +U_9 +U_18 +U_5 +C_12 +C_11 +C_9 +C_13 +C_14 +C_2 +C_3 +C_10 +C_4 +..X.X...X +......... +......... +....X.... +......... +......... +..X...X.. +......... +....X.... +X.X.X.X.. +......... diff --git a/cointoss-2-d.ctx b/cointoss-2-d.ctx new file mode 100644 index 000000000..795b6e8ee --- /dev/null +++ b/cointoss-2-d.ctx @@ -0,0 +1,137 @@ +B + +62 +8 + +191 +58 +180 +88 +108 +9 +93 +83 +188 +50 +141 +157 +87 +195 +118 +196 +14 +116 +59 +89 +61 +169 +179 +192 +167 +98 +73 +78 +186 +44 +100 +173 +53 +36 +12 +140 +166 +75 +194 +76 +6 +120 +70 +0 +95 +153 +74 +37 +46 +124 +56 +85 +126 +2 +54 +103 +31 +164 +163 +92 +79 +117 +9 +3 +4 +8 +7 +13 +1 +2 +........ +........ +...X...X +........ +.X..X.XX +......X. +........ +........ +........ +........ +...X...X +.......X +.......X +...X.... +...X..X. +...X.... +......X. +........ +.......X +.XXX..X. +......X. +......X. +........ +........ +........ 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+134 +39 +1 +146 +63 +84 +177 +0 +43 +125 +104 +95 +153 +74 +142 +46 +127 +11 +109 +138 +45 +114 +56 +32 +133 +147 +55 +182 +85 +189 +126 +2 +143 +178 +72 +170 +103 +91 +10 +65 +161 +129 +187 +31 +71 +164 +163 +64 +92 +23 +79 +160 +29 +150 +132 +att_0 +att_8 +att_6 +att_1 +att_2 +..... +.X.XX +X..X. +XX..X +...X. +..... +.X... +XX... +X..XX +.X.XX +...X. +..X.X +XX... +X..XX +..... +..... +X.... +.X.X. +..... +.X..X +XX.X. +XX... +XX.XX +..... +.X... +...XX +.X.X. +.X..X +X.... +X.XXX +....X +....X +.X.X. +XX... +.X.X. +.X.X. +X.... +XX... +X.... +X.... +X.... +X..X. +XX.X. +.X... +..X.X +.XX.X +.X..X +....X +.X..X +..X.X +.X.XX +X.X.X +..X.X +.X.XX +XXX.X +X.... +X.... +XXX.X +.X..X +X.... +XX..X +XXX.X +XX..X +XX... +.X.X. +..... +..... +..XXX +X.... +X..XX +XXXXX +XX.X. +.X.X. +XX... +..... +X..X. +X..X. +.X... +....X +....X +.XXXX +X...X +..X.X +....X +XX... +..... +X...X +..... +XX... +XX... +XX.X. +.X..X +...X. +..XXX +.X... +.X... +..XXX +X.X.X +X.... +.X... +XX... +....X +X...X +X..X. +XX... +...XX +..X.X +.X.XX +X..X. +....X +X.... +..... +....X +.X.XX +..X.X +....X +X...X +...XX +.XX.X +X..X. +.X..X +X.... +....X +X...X +X..X. +...X. +....X +.X..X +...X. +X.... +X.... +XX... +.X.XX +X...X +XX..X +.X... +.XX.X +.X.X. +XX... +..... +.X... +X.X.X +..XXX +XX.X. +.X.X. +X..X. +X...X +...XX +....X +.XX.X +....X +.X.XX +..X.X +...X. +XX... +XXX.X +X.... +XX... diff --git a/dolphins-d.ctx b/dolphins-d.ctx new file mode 100644 index 000000000..d9aa30dbd --- /dev/null +++ b/dolphins-d.ctx @@ -0,0 +1,87 @@ +B + +28 +26 + +U_58 +U_17 +U_3 +U_35 +U_28 +U_61 +U_42 +U_4 +U_62 +U_40 +U_32 +U_10 +U_24 +U_14 +U_60 +U_29 +U_57 +U_49 +U_9 +U_45 +U_21 +U_56 +U_23 +U_13 +U_12 +U_33 +U_59 +U_5 +A_37 +A_1 +A_13 +A_30 +A_12 +A_17 +A_53 +A_48 +A_41 +A_9 +A_24 +A_31 +A_47 +A_32 +A_19 +A_25 +A_56 +A_28 +A_44 +A_59 +A_20 +A_5 +A_36 +A_57 +A_22 +A_23 +.......................... +.......................... +.......................... +.......................... +.......................... +.......................... +.......................... +.........X................ +.......................... +X......................... +.......................... +.......................... +X......................... +.......................... +X........X................ +.......X.X.X.............. +.......................... +.......................... +.......................... +.......................... +X....X.X.X....X........... +.......................... +.......................... +.......................... +.......................... +.......................... +.......................... +.......................... diff --git a/drive_concepts_for_motorcars-d.ctx b/drive_concepts_for_motorcars-d.ctx new file mode 100644 index 000000000..4ec145f36 --- /dev/null +++ b/drive_concepts_for_motorcars-d.ctx @@ -0,0 +1,33 @@ +B + +5 +18 + +Conventional +All-wheel +Rear-wheel +Mid-engine +Front-wheel +E+ +C-l +E- +C-h +De+ +Dl+ +C-vl +E++ +S-u/n +Dl++ +Dl- +R+ +S-n +De++ +M-- +M- +R++ +E-- +X....X.....X...... +X..XXX..XX.X.X.X.. +.XX.XX...X...X.... +.XX.XX...X.XXXXX.X +XX..X.XX..XX....X. diff --git a/forum-romanum-d.ctx b/forum-romanum-d.ctx new file mode 100644 index 000000000..a33bd7871 --- /dev/null +++ b/forum-romanum-d.ctx @@ -0,0 +1,27 @@ +B + +8 +6 + +Basilica of Maxentius +Temple of Vesta +Arch of Septimus Severus +Temple of Antonius and Fausta +Curia +Phocas column +Temple of Castor and Pollux +Arch of Titus +GB2 +M2 +GB1 +B +M1 +M3 +...X.. +XXX.X. +.XXXX. +.XXXXX +...... +.XX.X. +XXXXXX +XXXXX. diff --git a/gewuerzplaner-d.ctx b/gewuerzplaner-d.ctx new file mode 100644 index 000000000..3d9379683 --- /dev/null +++ b/gewuerzplaner-d.ctx @@ -0,0 +1,62 @@ +B + +20 +17 + +Gedünsteter Fisch +Kräuterquark/Dips +Rindfleisch +Bratkartoffeln +Gebratener Fisch +Gulasch +Risotto/Paella +Kartoffelauflauf/-gratin +Bowle +Desserts +Püree +Käsegebäck +Gegrillter Fisch +Kuchen +Gebackener Fisch +Rouladen +Blechkartoffeln +Punch/Tee +Obstsalat +Kalbfleisch +Estragon gerebelt +Verschiedenes(Gruppierung) +Fisch(Gruppierung) +Paprika “Rosen” gemahlen +Gemüse(Gruppierung) +Oregano gerebelt +Saucen(Gruppierung) +Piment gemahlen +Curry gemahlen +Wacholderbeeren +Geflügel(Gruppierung) +Bohnenkraut gerebelt +Knoblauch granuliert +Kurkuma +Beifuß gemahlen +Koriander gemahlen +Majoran gerebelt +..X.....X...X.... +XX.X.X..X...XX.X. +........X...X.... +...X........X.... +..XX.X..X...X.... +...X........X.... +........X...X.... +................. +................. +................. +................. +................. +..X.....X...X.... +................. +..X.....X...X.... +................. +...X........X.... +................. +................. +........X...X.... diff --git a/living-beings-and-water-d.ctx b/living-beings-and-water-d.ctx new file mode 100644 index 000000000..c6ba10bab --- /dev/null +++ b/living-beings-and-water-d.ctx @@ -0,0 +1,22 @@ +B + +6 +5 + +dog +fish leech +corn +water weeds +bean +reed +has limbs +breast feeds +needs chlorophyll +needs water to live +lives on land +XX.XX +...X. +..XXX +..XX. +..XXX +..XXX diff --git a/myctx-d.ctx b/myctx-d.ctx new file mode 100644 index 000000000..b4f4afb55 --- /dev/null +++ b/myctx-d.ctx @@ -0,0 +1,17 @@ +B + +4 +4 + +3 +1 +353 +2 +3 +2344 +23423 +1 +X... +...X +.... +.... diff --git a/olympic-disciplines-d.ctx b/olympic-disciplines-d.ctx new file mode 100644 index 000000000..46854bae7 --- /dev/null +++ b/olympic-disciplines-d.ctx @@ -0,0 +1,66 @@ +B + +24 +13 + +Judo – Judo +Aquatics – Swimming +Sport Climbing – Sport Climbing +Cycling – Track +Golf – Golf +Handball – Handball +Rugby – Rugby Sevens +Volleyball – Volleyball +Baseball/Softball – Baseball/Softball +Cycling – Mountain Bike +Karate – Kumite +Cycling – BMX Racing +Fencing – Fencing +Gymnastics – Rhythmic +Volleyball – Beach Volleyball +Basketball – Basketball +Tennis – Tennis +Karate – Kata +Archery – Archery +Weightlifting – Weightlifting +Skateboarding – Skateboarding +Basketball – 3x3 +Gymnastics – Trampoline +Cycling – BMX Freestyle +female only events +indoor events +mixed events +male only events +has paralympic equivalent +individual competition +open events +part of >= 16 olympics +>= 10 events +water sport +part of >= 24 olympics +combat sport +>= 20 events +XXXXXX..X..X. +XXXXXX.XXXX.X +XX.X.X....... +XX.XXX.XX.X.. +X..X.X....... +XX.X......... +X..XX........ +XX.XX........ +X..X......... +X..X.X....... +XX.X.X.....X. +X..X.X....... +XX.XXX.XX.XX. +XX...X....... +X..X......... +XX.XX..X..... +X.XXXX.X..... +XX.X.X.....X. +X.XXXX.X...X. +XX.XXX.XX.X.. +X..X.X....... +XX.X......... +XX.X.X....... +X..X.X....... diff --git a/seasoning-planner-d.ctx b/seasoning-planner-d.ctx new file mode 100644 index 000000000..3d9379683 --- /dev/null +++ b/seasoning-planner-d.ctx @@ -0,0 +1,62 @@ +B + +20 +17 + +Gedünsteter Fisch +Kräuterquark/Dips +Rindfleisch +Bratkartoffeln +Gebratener Fisch +Gulasch +Risotto/Paella +Kartoffelauflauf/-gratin +Bowle +Desserts +Püree +Käsegebäck +Gegrillter Fisch +Kuchen +Gebackener Fisch +Rouladen +Blechkartoffeln +Punch/Tee +Obstsalat +Kalbfleisch +Estragon gerebelt +Verschiedenes(Gruppierung) +Fisch(Gruppierung) +Paprika “Rosen” gemahlen +Gemüse(Gruppierung) +Oregano gerebelt +Saucen(Gruppierung) +Piment gemahlen +Curry gemahlen +Wacholderbeeren +Geflügel(Gruppierung) +Bohnenkraut gerebelt +Knoblauch granuliert +Kurkuma +Beifuß gemahlen +Koriander gemahlen +Majoran gerebelt +..X.....X...X.... +XX.X.X..X...XX.X. +........X...X.... +...X........X.... +..XX.X..X...X.... +...X........X.... +........X...X.... +................. +................. +................. +................. +................. +..X.....X...X.... +................. +..X.....X...X.... +................. +...X........X.... +................. +................. +........X...X.... diff --git a/southern-woman-d.ctx b/southern-woman-d.ctx new file mode 100644 index 000000000..4ac3435d3 --- /dev/null +++ b/southern-woman-d.ctx @@ -0,0 +1,39 @@ +B + +12 +10 + +Frances Anderson +Flora Price +Sylvia Avondale +Ruth DeSand +Theresa Anderson +Helen Lloyd +Eleanor Nye +Olivia Carleton +Dorothy Murchison +Nora Fayette +Katherina Rogers +Pearl Oglethorpe +E7 +E12 +E1 +E9 +E8 +E2 +E10 +E13 +E4 +E14 +....X..... +...X...... +XX.XX.XX.X +X..XX..... +X..XXX..X. +XX..X.X... +X...X..... +...X...... +...XX..... +XX.X..XX.X +.X.XX.XX.X +...XX..... diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index e5b49a574..c9beb89ed 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -6,7 +6,7 @@ ;; the terms of this license. ;; You must not remove this notice, or any other, from this software. -#(ns conexp.fca.decompositions +(ns conexp.fca.decompositions (:require [conexp.base :refer :all] [conexp.math.algebra :refer :all] [conexp.io.contexts :refer :all] @@ -63,6 +63,8 @@ rest-attr attr object-next true] +(println (count (objects subctx))) + (let [new-obj (first (filter #(distributive? (concept-lattice (add-obj subctx % incidence))) rest-objs)) new-attr (first (filter #(distributive? (concept-lattice (add-attr subctx % incidence))) rest-attr))] @@ -85,8 +87,36 @@ ) ))) - - - -;(def ctx (rad-context "testing-data/Bird-Diet.ctx")) +(for [ctx ctx-list] (println (concept-lattice (read-context ctx)))) + +(def pair-list (for [ctx ctx-list] (libkin-decomposition-pairs (concept-lattice (read-context ctx))))) + +(def ctx-list #{"animals-d.ctx" + "bird-diet-d.ctx" + "bodiesofwater-d.ctx" + "booth-d.ctx" + "brunson-club-d.ctx" + "cointoss-2-d.ctx" + "diagnosis-d.ctx" + "digits-d.ctx" + "dirichlet-1-d.ctx" + "dolphins-d.ctx" + "drive_concepts_for_motorcars-d.ctx" + "forum-romanum-d.ctx" + "gewuerzplaner-d.ctx" + "living-beings-and-water-d.ctx" + "myctx-d.ctx" + "olympic-disciplines-d.ctx" + "seasoning-planner-d.ctx" + "southern-woman-d.ctx" + "testcontext-d.ctx" + "triangles-d.ctx" + "wood-properties-d.ctx" + "zoo-d.ctx"}) + + + +;(use 'conexp.io.contexts) +;(def ctx (read-context "testing-data/Bird-Diet.ctx")) ;(make-context #{} #{} (incidence ctx)) +;(write-context :burmeister (distributive-exploration (read-context "testing-data/Bird-Diet.ctx") ectx) "ird-diet-d.ctx") diff --git a/testcontext-d.ctx b/testcontext-d.ctx new file mode 100644 index 000000000..35edfbf71 --- /dev/null +++ b/testcontext-d.ctx @@ -0,0 +1,14 @@ +B + +3 +3 + +3 +1 +2 +d +a +b +.XX +X.. +X.X diff --git a/triangles-d.ctx b/triangles-d.ctx new file mode 100644 index 000000000..ac3162cff --- /dev/null +++ b/triangles-d.ctx @@ -0,0 +1,21 @@ +B + +6 +4 + +T6 +T3 +T7 +T2 +T5 +T1 +right-angled +scalene +equilateral +isosceles +.X.X +.X.. +XX.. +XX.X +.X.. +.X.X diff --git a/wood-properties-d.ctx b/wood-properties-d.ctx new file mode 100644 index 000000000..7de5a258e --- /dev/null +++ b/wood-properties-d.ctx @@ -0,0 +1,45 @@ +B + +14 +12 + +kirche +linde +wkiefer +nuß +rkastanie +pflaume +ulme +rbuche +weide +eiche +olive +zkiefer +buchsbaum +esche +fjähr +s +biegs +elas +arbs +n_elas +k_s +r_s +fpor +reißt +brüchig +k +XX....X.X... +X.XX....X... +............ +X.XX..X.X... +XX......X... +X.....X.X... +.X.......... +XXXXX..XX... +..XX........ +.X....X..... +X.....X.X... +X.....X.X... +XX......X... +.XXX..X..... diff --git a/zoo-d.ctx b/zoo-d.ctx new file mode 100644 index 000000000..103b2486f --- /dev/null +++ b/zoo-d.ctx @@ -0,0 +1,134 @@ +B + +54 +21 + +reindeer +aardvark +slowworm +gull +parakeet +wasp +polecat +crow +platypus +wolf +skua +mole +vole +hare +boar +hawk +cavy +antelope +sparrow +lark +goat +wallaby +squirrel +wren +puma +mongoose +pony +fruitbat +bear +pussycat +lynx +girl +dove +gorilla +honeybee +elephant +calf +duck +mink +opossum +leopard +buffalo +lion +pheasant +giraffe +cheetah +skimmer +oryx +vampire +deer +hamster +raccoon +chicken +kiwi +[catsize 0] +[predator 1] +[feathers 0] +[fins 0] +[fins 1] +[hair 0] +[breathes 1] +[toothed 0] +[leg 8] +[backbone 1] +[type 4] +[backbone 0] +[type 6] +[leg 6] +[type 5] +[eggs 0] +[type 3] +[type 7] +[leg 0] +[animal-name 1] +[leg 5] +.XXX.X...X.........X. +.XXX.X...X.........X. +XX.X.X...X.....XX.X.. +X..X.....X.....X..... +X..X.....X.....X..... +X..X.XXX.X..XX.X...X. +.XXX.X...X.........X. +X..X.....X.....X..... +...X.X...X.........X. +.XXX.X...X.........X. +X..X.....X.....X..... +XXXX.X...X.........X. +XXXX.X...X.........X. +XXXX.X...X.........X. +.XXX.X...X.........X. +X..X.....X.....X..... +XXXX.X...X.........X. +.XXX.X...X.........X. +X..X.....X.....X..... +X..X.....X.....X..... +.XXX.X...X.........X. +.XXX.X...X.........X. +XXXX.X...X.........X. +X..X.....X.....X..... +.XXX.X...X.........X. +.XXX.X...X.........X. +.XXX.X...X.........X. +XXXX.X...X.........X. +.XXX.X...X.........X. +.XXX.X...X.........X. +.XXX.X...X.........X. +.XXX.X...X.........X. +X..X.....X.....X..... +.XXX.X...X.........X. +X..X.XXX.X..XX.X...X. +.XXX.X...X.........X. +.XXX.X...X.........X. +X..X.....X.....X..... +.XXX.X...X.........X. +XXXX.X...X.........X. +.XXX.X...X.........X. +.XXX.X...X.........X. +.XXX.X...X.........X. +X..X.....X.....X..... +.XXX.X...X.........X. +.XXX.X...X.........X. +X..X.....X.....X..... +.XXX.X...X.........X. +XXXX.X...X.........X. +.XXX.X...X.........X. +XXXX.X...X.........X. +.XXX.X...X.........X. +X..X.....X.....X..... +X..X.....X.....X..... From c3488d1a2e32716c2d8826148b52aa0c7359553b Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 7 Sep 2023 19:04:35 +0200 Subject: [PATCH 083/117] Implemented Methods for Generating Distributive Lattice from three Elements and Testing if an Element is Neutral. --- src/main/clojure/conexp/fca/metrics.clj | 894 +++++++++++++++++++++++- 1 file changed, 892 insertions(+), 2 deletions(-) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 6068d1650..ef0e7e81f 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -19,7 +19,821 @@ context-object-closure object-derivation random-context objects attributes - context? concept?]] + context? concept? + diag-context + adiag-context + rand-context]];temp + [exploration :refer :all] + [fast :refer [with-binary-context + to-bitset + bitwise-context-attribute-closure + bitwise-object-derivation + bitwise-attribute-derivation concepts]] + [implications :refer :all] + [lattices :refer [inf sup lattice-base-set make-lattice make-lattice-nc + concept-lattice lattice-order extract-context-from-bv + distributive?]]] + [clojure.set :as set] + [conexp.math.util :refer [eval-polynomial binomial-coefficient]]) + (:import [conexp.fca.lattices Lattice] + [java.util ArrayList BitSet])) + + +;; help (outsource me) +(defn log2 [n] + (/ (Math/log n) (Math/log 2))) + +;;; Concept Stability and the like + +(defn concept-stability + "Compute the concept stability of `concept' in `context'." + [context concept] + + (assert (context? context) + "First argument must be a formal context.") + (assert (and (vector? concept) + (= 2 (count concept)) + (concept? context concept)) + "Second argument must be a formal concept of the given context.") + + (let [[extent intent] [(first concept) (second concept)] + counter (fn counter + ;; Perform depth-first search to count all subsets of + ;; `extent' whose derivation in context yields `intent'. + ;; For this we keep the list `fixed-included' of already + ;; considered elements to be included in the target + ;; subset of `extent', and the list `unfixed' of + ;; unconsidered elements for which it is still to be + ;; decided of whether they will be included or not. + [fixed-included unfixed] + (if (empty? unfixed) + 1 + (let [some-element (first unfixed)] + (+ (counter (conj fixed-included some-element) + (disj unfixed some-element)) + (if (= intent + (object-derivation context + (union fixed-included + (disj unfixed some-element)))) + (counter fixed-included (disj unfixed some-element)) + 0)))))] + (/ (counter #{} extent) + (expt 2 (count extent))))) + +(defn separation-index + "The concept separation is an importance measure for concepts. It + computes the size AxB (c-inc) relative to uncovered incidences Ax(M-B) + and (G-A)xB (o-inc). Max value is 1. + + Klimushkin M., Obiedkov S., Roth C. (2010) Approaches to the + Selection of Relevant Concepts in the Case of Noisy Data. In: Kwuida + L., Sertkaya B. (eds) Formal Concept Analysis. ICFCA 2010. Lecture + Notes in Computer Science, vol 5986. Springer, Berlin, + Heidelberg. https://doi.org/10.1007/978-3-642-11928-6_18" + [context concept] + (assert (context? context) + "First argument must be a formal context.") + (assert (and (vector? concept) + (= 2 (count concept)) + (concept? context concept)) + "Second argument must be a formal concept of the given context.") + (let [[extent intent] concept + c-inc (* (count extent) (count intent)) + g-inc (reduce + + (map + #(count (object-derivation context #{%})) + extent)) + a-inc (reduce + + (map #(count (attribute-derivation context #{%})) + intent)) + o-inc (- (+ g-inc a-inc) + c-inc)] ; is at least c-inc large + (/ c-inc o-inc))) + +(def ^:dynamic *fast-computation* + "Enable computation of concept probability with floating point arithmetic + instead of rationals" + nil) + +(defn concept-probability + "Compute the probability of a `concept' in `context' 𝕂 in the following manner. + Let pₘ be the relative frequence of attribute m in context. The + probability of a subset B ⊆ M in 𝕂 is the product of all pₘ for m ∈ B. + Then the probability of a concept is defined by pr(A,B) := pr(B=B'') + which is ∑_{k=0}^n {n choose k}·p_Bᵏ·(1-p_B)ⁿ⁻ᵏ·∏_{m ∈ M ∖ B}(1-p_mᵏ)." + [context concept] + (let [nr_of_objects (count (objects context)) + n (if *fast-computation* (double nr_of_objects) nr_of_objects) + M (attributes context) + B (second concept) ; intent of concept + P_M_B (mapv #(/ (count (attribute-derivation context #{%})) n ) (difference M B)) + p_B (r/fold * (map #(/ (count (attribute-derivation context #{%})) n) B)) + one_minus_p_B_n (expt (- 1 p_B) n)] + (if (not= (double p_B) 1.0) ;; if concept's extent= n + (loop [k 1 ;; since for k=0 the last term is 0, we can start with 1 + result 0 + binomial n ;; since k=0 the start binomial is n + p_B_k p_B + one_minus_p_B_k (/ one_minus_p_B_n (- 1 p_B)) + P_M_B_k P_M_B ] + (if (or (== k n) (== p_B_k 0)) ;; either done or underflowed probability (double) + result + (let [new_res + (* binomial p_B_k one_minus_p_B_k + (r/fold * (map #(- 1 %) P_M_B_k)))] + (recur + (inc k) + (+ new_res result) + (* binomial (/ (- n k) (inc k))) + (* p_B_k p_B) + (/ one_minus_p_B_k (- 1 p_B)) + (mapv (partial *) P_M_B_k P_M_B))))) + 1))) + + +;;; Robustness of Concepts + +(defn- concept-robustness-add-next-entry + "Helper-function for `concept-robustness-polynomial'. + + This function computes the value e(Y,`concept'), based on the already computed + values e(Z,`concept'), which are given in the second parameter `cache' in the + form [Z, e(Z, `concept')]. + + This function is needed in the algorithm on page 19 in \"Finding Robust + Itemsets under Subsampling\" from Tatti, Moerchen, and Calders." + [concept cache] + (let [newvalue (reduce + (fn [x V] (- x (second V))) + 0 + (filter #(subset? (second (first %)) (second concept)) + cache))] + (conj cache [concept, newvalue]))) + +(defn concept-robustness-polynomial + "Return the coefficients of the robustness polynomial of `concept'. + + For the given `concept' of a context, the coefficients of the polynomial p + corresponding to the robustness is computed by using the seq `concepts' of + all concepts of the context. The optional boolean parameter `sorted?' allows + to declare the seq of concepts as being already sorted by increasing + attribute-set. Thus if v is the result of (robustness-polynomial concept + concepts), then (eval-polynomial v (- 1 alpha)) computes the robustness with + parameter alpha. + + For details see \"Finding Robust Itemsets under Subsampling\" from Tatti, + Moerchen, and Calders, pages 17–19." + ([concept concepts sorted?] + (let [B (second concept) + used-concepts (drop 1 (if sorted? + (filter #(subset? B (second %)) concepts) + (sort-by #(count (second %)) + (filter #(subset? B (second %)) + concepts)))) + ;; store for all subconcepts (C_A,C_B) of concept the vector [C, e(C_B, concept)] + concepts-with-values (reduce + (fn [x y] + (concept-robustness-add-next-entry y x)) + [[concept, 1]] + used-concepts) + sup (count (first concept))] + ;; use the above computed values [C, e(C_B, concept)] to compute the polynomial + (reduce + (fn [old-coefficients entry] + (let [index (- sup (count (first (first entry))))] + (assoc old-coefficients + index (+ (nth old-coefficients index) (second entry))))) + (vec (take (+ 1 sup) (repeat 0))) + concepts-with-values))) + ([concept concepts] + (concept-robustness-polynomial concept concepts false))) + +(defn concept-robustness + "Computes the robustness of a `concept' in a context with parameter `alpha' by + using the seq `concepts' consisting of all concepts of the context. The + optional boolean parameter `sorted?' allows to declare the seq of concepts as + beeing already sorted by increasing size of the attribute set. This function + uses the function concept-robustness-polynomial." + ([concept concepts alpha sorted?] + (assert (and (number? alpha) + (<= 0 alpha 1)) + "Third argument must be between 0 and 1!") + (eval-polynomial (concept-robustness-polynomial concept concepts sorted?) (- 1 alpha))) + ([concept concepts alpha] + (concept-robustness concept concepts alpha false))) + +(defn average-concept-robustness + "Takes the seq `concepts' consisting of all concepts of a context and computes + the average concept robustness with parmater `alpha'." + [concepts alpha] + (assert (and (number? alpha) + (<= 0 alpha 1)) + "Second argument must be between 0 and 1!") + (let [sorted-concepts (sort-by + #(count (second %)) + concepts) + n (count sorted-concepts) + robustness-values (map + #(concept-robustness + (nth sorted-concepts %) + (drop % sorted-concepts) + alpha + true) + (range 0 n))] + (/ (reduce + robustness-values) n))) + + +;;; Similarity Measures for Concepts (implemented by Anselm von Wangenheim) + +(defn jaccard-index + "Computes the Jaccard index of two sets. This is |x ∩ y| / |x ∪ y|. + Returns 1 if both sets are empty." + [x y] + (if (and (empty? x) (empty? y)) + 1 + (/ (count (intersection x y)) (count (union x y))))) + +(defn sorensen-coefficient + "Computes the Sorensen coefficient of two sets. + This is 2 * |x ∩ y| / (|x| + |y|). + Returns 1 if both sets are empty." + [x y] + (if (and (empty? x) (empty? y)) + 1 + (/ (* 2 (count (intersection x y))) (+ (count x) (count y))))) + +(defn weighted-concept-similarity + "Computes a weighted concept similarity for a given similatity measure `sim', + two concepts [`c1' `c2'] and an optional weight `w' (default is 1/2). + + That is the weighted average of the similarity of the extents/object sets + (weight `w') and the intents/attribute sets (weight 1-`w'). + + This is from Alqadah, F. & Bhatnagar, R. (2011), 'Similarity measures in + formal concept analysis.', Ann. Math. Artif. Intell. 61 (3), 249, + https://doi.org/10.1007/s10472-011-9257-7" + ([sim [c1 c2]] (weighted-concept-similarity sim [c1 c2] (/ 1 2))) + ([sim [c1 c2] w] + (assert (and (number? w) + (<= 0 w 1)) + "Thrid argument must be between 0 and 1!") + (+ + (* w (sim (c1 0) (c2 0))) + (* (- 1 w) (sim (c1 1) (c2 1)))))) + + + +;;; Concept stability + +(defn mcs-stability-approximation + "Approximates concept stability with Markov Chains." + [ctx concept sample-size] + (let [counter (atom 0)] + (doall + (for [i (range sample-size)] + (let [prem (first concept) + concl (second concept) + limit (count concl)] + (if (= (attribute-derivation ctx + (take (rand-int limit) + (shuffle concl))) + prem) + (swap! counter inc))))) + (/ @counter sample-size))) + +(defn lds-stability-approximation + "Approximates concept stability with Low-Discrepancy Sampling. The function + takes a context and concept, the sample-size and base (both as integer). + An additional argument may be given to choose the sampling method. + The options are: + :sobol One-dimensional Sobol Sequence (default) + :svdc Scrambled Van der Corput Sequence + + Function based on 'An Efficient Approximation of Concept + Stability Using Low-Discrepancy Sampling' Ibrahim; Missaoui 2018 + https://link.springer.com/chapter/10.1007/978-3-319-91379-7_3 " + ([ctx concept sample-size base] + (lds-stability-approximation ctx concept sample-size base :sobol)) + ([ctx concept sample-size base sampling-method] + (let [lds (atom []) + counter (atom 0) + intent (second concept) + intent-size (count intent) + powerset (subsets intent)] + (doall + (for [i (range sample-size)] + (swap! lds conj (case sampling-method + :sobol (generate-sobol i) + :svdc (generate-svdc i base) + (generate-sobol i))))) + (doall + (for [element @lds] + (let [position (int (+ (* intent-size element) 0.5)) + subset (nth powerset position)] + (if (= (first concept) + (attribute-derivation ctx subset)) + (swap! counter inc))))) + (/ @counter sample-size)))) + +;;; standard lattice properties to some degree + +(defn satisfying-triples + "Given lattice lat, compute triples (a,b,c)∈L³ (pairwise different) + such that they fullfil a given condition. The triples may be + filtered beforehand using prefilter." + ([^Lattice lat condition] + (let [base (into [] (lattice-base-set lat))] + ;; (filter condition (filter prefilter (permuted-combinations base 3))))) + (filter condition (permuted-combinations base 3)))) + ([lat condition prefilter] + (let [base (into [] (lattice-base-set lat))] + (filter condition (filter prefilter (permuted-combinations base 3)))))) + + +(defn distributive-triples + "Given lattice lat, compute triples (x,y,z)∈L³ (pairwise different) + such that they fullfil the distributive property + x∨(y∧z)=(x∨y)∧(x∨z)." + ([^Lattice lat] + (distributive-triples lat (fn [x] true))) + ([^Lattice lat prefilter] + (let [inf (inf lat), + sup (sup lat)] + (satisfying-triples lat (fn [[x y z]] + (= (sup x (inf y z )) + (inf (sup x y) (sup x z)))) + prefilter)))) + +(defn modular-triples + "Given lattice lat, compute triples (x,y,z)∈L³ (pairwire different) + such that they fullfil the modular property x ≤ z ⇒ + x∨(y∧z)=(x∨y)∧z." + ([lat] + (modular-triples lat (fn [x] true))) + ([lat prefilter] + (let [inf (inf lat), + sup (sup lat), + ord (lattice-order lat) + base (into [] (lattice-base-set lat))] + (satisfying-triples lat (fn [[x y z]] + (if (ord x z) ;; if x≤y + (= ;; check x∨(y∧z)=(x∨y)∧z + (sup x (inf y z)) + (inf (sup x y) z)) + true)) + prefilter)))) ;; else always true + +(defn distributivity-degree + "Computes the number of triples (a,b,c)∈L³ (pairwise different) + that fullfil the distributivity law and divides it by the number of + possible pw different triples." + [lat] + (let [n (count (lattice-base-set lat))] + (if (< n 3) + 1 ;; in case we have less than 3 elements we have distributivity + (/ (count (distributive-triples lat)) + (* 6 (binomial-coefficient n 3)))))) + +(defn modularity-degree + "Computes the number of triples (a,b,c)∈L³ (pairwise different) + that fullfil the modularity law and divides it by the number of + possible pw different triples. (tbc later on)" + [lat] + (let [n (count (lattice-base-set lat))] + (if (< n 3) + 1 ;; in case we have less than 3 elements we have modularity + (/ (count (modular-triples lat)) + (* 6 (binomial-coefficient n 3)))))) + +(defn elements-distributivity + "Computes the number of triples (a,b,c)∈L³ (pw different) where either + a=e, b=e, or c=e, that fullfil the modularity law. This number is + then divided it by the number of possible pw different triples of such kind." + [lat e] + (assert (contains? (lattice-base-set lat) e)) + (let [n (count (lattice-base-set lat)), + filterfunc (fn [[x y z]] (or (= x e) (= y e) (= z e)))] + (/ (count (distributive-triples + lat filterfunc)) + (* 6 (binomial-coefficient (- n 1) 2))))) + +(defn elements-modularity + [lat e] + (assert (contains? (lattice-base-set lat) e)) + (let [n (count (lattice-base-set lat))] + (/ (count (modular-triples lat (fn [[x y z]] (or (= x e) (= y e) (= z e))))) + (* 6 (binomial-coefficient (- n 1) 2))))) + +;;; Relevant Attributes (Objects) et Al + +(defn attribute-information-entropy + "Computes the attribute-information-entropy for a given context 𝕂using the formula + (∑_{m ∈ M} 1-{m}''/|M|)/|M|, see https://doi.org/10.1007/978-3-030-23182-8_8" + [ctx] + (let [M (attributes ctx) + nr_of_attributes (count M)] + (/ (- nr_of_attributes + (r/fold + (pmap + (fn [m] (/ (count (context-attribute-closure ctx #{m})) + nr_of_attributes)) + M))) + nr_of_attributes))) + +(defn object-information-entropy + "Computes the object-information-entropy for a given context 𝕂using the formula + (∑_{g ∈ G} 1-{g}''/|G|)/|G|, see https://doi.org/10.1007/978-3-030-23182-8_8" + [ctx] + (attribute-information-entropy (dual-context ctx))) + +(defn information-entropy + "Computes the mean entropy of context ctx based on the equal + weighted sum of attribute-information-entropy and + object-information-entropy." + [ctx] + (/ (+ (attribute-information-entropy ctx) (object-information-entropy ctx)) 2)) + + +(defn shannon-attribute-information-entropy + "Computes the Shannon-attribute-information-entropy for a given context 𝕂using the formula + ∑_{m ∈ M} -{m}''/|M|· log₂ ({m}''/|M|), see https://doi.org/10.1007/978-3-030-23182-8_8" + [ctx] + (let [M (attributes ctx) + nr_of_attributes (count M)] + (r/fold + (pmap (fn [x] (- (* x (log2 x)))) + (pmap + (fn [m] (/ (count (context-attribute-closure ctx #{m})) + nr_of_attributes)) + M))))) + +(defn shannon-object-information-entropy + "Computes the Shannon-object-information-entropy for a given context 𝕂using the formula + ∑_{g ∈ G} -{g}''/|G|· log₂ ({g}''/|G|), see https://doi.org/10.1007/978-3-030-23182-8_8" + [ctx] + (shannon-attribute-information-entropy (dual-context ctx))) + +(defn shannon-attribute-information-entropy-fast + "Computes the Shannon-attribute-information-entropy for a given + context 𝕂using the formula ∑_{m ∈ M} -{m}''/|M|· log₂ ({m}''/|M|), + see https://doi.org/10.1007/978-3-030-23182-8_8. This implementation + resorts to bit vectors in order to increase the computation + speed. This conversion is not adviced for small data sets. " + [ctx] + (with-binary-context ctx + (let [a-closure-counts + (pmap (fn [y] + (let [^BitSet bs (BitSet.)] + (.set bs y) + (bitwise-context-attribute-closure + incidence-matrix + object-count + attribute-count + bs))) + (range attribute-count))] + (- + (r/fold + (map (fn [x] (* (/ (.cardinality ^BitSet x) ^long attribute-count) + (log2 (/ (.cardinality ^BitSet x) ^long attribute-count)))) + a-closure-counts)))))) + + +(defn shannon-object-information-entropy-fast + "Computes the Shannon-object-information-entropy for a given context 𝕂using the formula + ∑_{g ∈ G} -{g}''/|G|· log₂ ({g}''/|G|), see https://doi.org/10.1007/978-3-030-23182-8_8" + [ctx] + (shannon-attribute-information-entropy-fast (dual-context ctx))) + +(defn shannon-information-entropy + "Computes the mean shannon-entropy of context ctx based on the equal + weighted sum of attribute-information-entropy and + object-information-entropy." + [ctx] + (/ (+ (shannon-attribute-information-entropy ctx) + (shannon-object-information-entropy ctx)) 2)) + +(defn shannon-information-entropy-fast + "Computes the mean shannon-entropy of context ctx based on the equal + weighted sum of attribute-information-entropy and + object-information-entropy." + [ctx] + (/ (+ (shannon-attribute-information-entropy-fast ctx) + (shannon-object-information-entropy-fast ctx)) 2)) + +(defn extent-label-function + "Computes the label for given g ∈ G, i.e., the natural number n such + that n=|{c ∈ 𝔅(𝕂) ∣ g ∈ ext(c)}|, see + https://doi.org/10.1007/978-3-030-23182-8_8" + ([ctx g] + (extent-label-function ctx (concepts :in-close ctx) g)) + ([ctx concepts g] + (count + (filter (fn [x] (contains? (first x) g)) + concepts)))) + +(defn intent-label-function + "Computes the label for given m ∈ M, i.e., the natural number n such + that n=|{c ∈ 𝔅(𝕂) ∣ m ∈ int(c)}|, see + https://doi.org/10.1007/978-3-030-23182-8_8" + ([ctx m] + (extent-label-function ctx (concepts :in-close ctx) m)) + ([ctx concepts m] + (count + (filter (fn [x] (contains? (second x) m)) + concepts)))) + +(defn attribute-removal-robust-concepts + "Computes the set of concepts {c ∈ 𝔅(𝕂) ∣ (int(c) ∖ A)' = ext(c)} + for some attribute set A ⊆ M." + ([ctx A] + (attribute-removal-robust-concepts ctx (concepts :in-close ctx) A)) + ([ctx theconcepts A] + (into [] (r/filter (fn [x] (= + (attribute-derivation ctx (difference (second x) A)) + (first x))) + theconcepts)))) + +(defn object-removal-robust-concepts + "Computes the set of concepts {c ∈ 𝔅(𝕂) ∣ (ext(c) ∖ A)' = int(c)} + for some attribute set A ⊆ G." + ([ctx A] + (object-removal-robust-concepts ctx (concepts :in-close ctx) A)) + ([ctx theconcepts A] + (into [] (r/filter (fn [x] (= + (object-derivation ctx (difference (first x) A)) + (second x))) + theconcepts)))) + + +(defn relative-relevance + "Computes for formal context (G,M,I) the relative relevance of + attribute set A ⊆ M, using the formula from Proposition 3.5 in + https://doi.org/10.1007/978-3-030-23182-8_8, i.e., + r(A)=1-∑_{c∈𝔅(𝕂_A)}|ext(c)|/∑_{c∈𝔅(𝕂)}|ext(c)|, + where 𝔅(𝕂_A)={c∈𝔅(𝕂)∣(int(c)∖A)'=ext(c)}" + ([ctx A] + (relative-relevance ctx (concepts :in-close) A)) + ([ctx theconcepts A] + (let [extsum (r/fold + (map (fn [x] (count (first x))) theconcepts))] + (- 1 + (->> theconcepts + (filter + (fn [x] (= (count + (attribute-derivation ctx (difference (second x) A))) + (count (first x))))) + (pmap (fn [x] (count (first x)))) + (r/fold +) + (* (/ 1 extsum))) + )))) + +(defn relative-relevance-fast + "Compute relative-relevance using bitsets" + [ctx theconcepts A] + (with-binary-context ctx + (let [o-prime (partial bitwise-object-derivation incidence-matrix object-count attribute-count) + a-prime (partial bitwise-attribute-derivation incidence-matrix object-count attribute-count) + theextents (pmap (fn [x] (to-bitset object-vector (first x))) theconcepts) + theatts (to-bitset attribute-vector A)] + (- 1 + (/ + (r/fold + (map (fn [x] + (if (= + (let [thing (o-prime x)] + (.andNot thing theatts) ;; remove attribute set + (.cardinality (a-prime thing))) + (.cardinality x)) + (.cardinality x) + 0)) + theextents)) + (r/fold + (map (fn [x] (.cardinality x)) theextents))))))) + +(defn next-maximal-relevant + "Given a formal context (G,M,I), an attribute set A ⊆ M, this + functions computes the most relevant m ∈ M ∖ A with respect to relative-relevance." + ([ctx theconcepts] (next-maximal-relevant ctx theconcepts #{})) + ([ctx theconcepts A] + (let [atts (attributes ctx) + available-atts (difference atts A) + obs (objects ctx)] + (apply max-key (fn [x] (relative-relevance-fast ctx theconcepts (union A #{x}))) + available-atts)))) + +(defn next-n-maximal-relevant + "Based on next-maximal-relevant, compute the the next n maximal + relevant features in a consekutive manner. Please be advised, this + is not necessiraly equivalent to compute the subset N ⊆ M with |N|=n + being the most relevant wrt relative-relevance." + ([ctx theconcepts n] + (next-n-maximal-relevant ctx theconcepts n #{})) + ([ctx theconcepts n A] + (loop [[counter resultset] [0 []]] + (if (< counter n) + (recur [(inc counter) + (conj resultset + (next-maximal-relevant ctx theconcepts (set (union resultset A))))]) + resultset)))) + +(defn n-maximal-relevant + "Based on relative-relevance, compute the the subset N ⊆ M with |N|=n, + such that there is no L ⊆ M with r(N) k n) + result + (recur + (inc k) + (conj result + (let [atts (attributes ctx) + available-atts (difference atts (union A result)) + obs (objects ctx)] + (apply max-key (fn [x] + (let [pctx (make-context obs (union #{x} result A) (incidence ctx))] + (* + (count (concepts :in-close pctx)) + (object-information-entropy pctx)))) + available-atts))))))) + +(defmethod next-n-maximal-relevant-approx :shannon + ([_ ctx n] + (next-n-maximal-relevant-approx :shannon ctx n #{})) + ([_ ctx n A] + (loop [k 1 + result []] + (if (> k n) + result + (recur + (inc k) + (conj result (let [atts (attributes ctx) + available-atts (difference atts (union A result)) + obs (objects ctx)] + (apply max-key (fn [x] + (let [pctx (make-context obs (union #{x} A result) (incidence ctx))] + (* + (count (concepts :in-close pctx)) + (shannon-object-information-entropy-fast pctx)))) + available-atts)))))))) + + +(defn nRandomAtts + [ctx n] + (let [atts (attributes ctx)] + (take n (shuffle atts)))) + +;; (defn rel-consistency ??? +;; "Computes the relative consistency of a subset $N ⊆ M$ with respect to +;; a given formal context (G,M,I), and some attribute subset N ⊆ M" +;; [ctx N] +;; (let [G (objects ctx) +;; M (attributes ctx) +;; MN (difference M N) +;; ctx-N (make-context G N (incidence ctx)) +;; ctx-MN (make-context G MN (incidence ctx))] +;; (let [derive-N (fn [x] (context-object-closure ctx-N x)) +;; derive-MN (fn [x] (context-object-closure ctx-MN x))] +;; (/ +;; (count (filter (fn [x] (subset? (derive-N #{x}) (derive-MN #{x}))) G)) +;; (count G) +;; )))) + +;; ) + + +(defn generate-from-triple [triple lat] + + (let [stage1-meets (for [a triple b triple] (inf lat a b)) + stage1-joins (for [a triple b triple] (sup lat a b)) + + stage2-meets (for [a stage1-joins b stage1-joins] (inf lat a b)) + stage2-joins (for [a stage1-meets b stage1-meets] (sup lat a b)) + + final-meet (inf lat stage1-joins) + + ground-set (set/union stage1-meets + stage1-joins + stage2-meets + stage2-joins + final-meet) + order-function ;tbt + ] +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.metrics + (:require [clojure.core.reducers :as r] + [clojure.math.combinatorics :refer [permuted-combinations combinations]] + ;; [clojure.math.numeric-tower :refer [log]] + [conexp.base :refer :all] + [conexp.math.markov :refer :all] + [conexp.fca + [contexts :refer [make-context incidence dual-context + attribute-derivation + context-attribute-closure + context-object-closure + object-derivation random-context + objects attributes + context? concept? + adiag-context + rand-context]];temp [exploration :refer :all] [fast :refer [with-binary-context to-bitset @@ -786,11 +1600,87 @@ ;; ) +;returns destributive lattice generated by the concepts in "triple" +;tripe must be a collection of three concepts in "lat" +(defn generate-from-triple [triple lat] + + (let [stage1-meets (for [a triple b triple] ((inf lat) a b)) + stage1-joins (for [a triple b triple] ((sup lat) a b)) + + stage2-meets (for [a stage1-joins b stage1-joins] ((inf lat) a b)) + stage2-joins (for [a stage1-meets b stage1-meets] ((sup lat) a b)) + + final-meet ((inf lat) ((inf lat) (first stage1-joins) (second stage1-joins)) (last stage1-joins)) + + base-set (set/union stage1-meets + stage1-joins + stage2-meets + stage2-joins + final-meet) + ] + + (make-lattice-nc base-set + (lattice-order lat) + (inf lat) + (sup lat))) +) + +;verifies if "concept" is a neutral element in "lat" +(defn neutral? [concept lat] + (let [base-set (lattice-base-set lat)] + (some identity (for [x base-set y base-set] (distributive? (generate-from-triple [concept x y] lat)))) +)) + +;return all neutral elements in "lat" +(defn neutral-concepts [lat] + (let [base-set (lattice-base-set lat)] + (filter #(neutral? % lat) base-set) +) +) + +;retruns a complement of "concept" in "lat" +(defn complemnt [concept lat] + (let [base-set (lattice-base-set lat) + top ]) + + +) + +;meets: +x-y +x-z +y-z +x-y-z + +x+y-x+z +x+y-y+z +x+z-y+z + +;joins: +x+y +x+z +y+z +x+y+z + +x-y+x-z +x-y+y-z +x-z+y-z + +x-y+x-z+y-z + +;test +(def ctx (make-context #{1 2 3 4 5} + #{"A" "B" "C" "D" "E"} + #{[1 "A"] [2 "A"] [2 "B"] [3 "B"] [3 "C"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) +(def lat (concept-lattice ctx)) +((inf lat2) [#{1} 0] [#{2} 0]) + +(def lat2 (generate-from-triple [[#{5} #{"E" "C" "D"}] [#{4 3} #{"C" "B"}] [#{4 2} #{"B" "A"}]] lat)) ;;; -nil + nil From 1075667893781166762bfb39192c9152e2afcaf0 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Fri, 8 Sep 2023 21:10:22 +0200 Subject: [PATCH 084/117] Added Functions for Libkin Decomposition. --- src/main/clojure/conexp/fca/metrics.clj | 79 +++++++++++++++++-------- 1 file changed, 55 insertions(+), 24 deletions(-) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index ef0e7e81f..8ba65e1e0 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -1604,32 +1604,37 @@ ;tripe must be a collection of three concepts in "lat" (defn generate-from-triple [triple lat] - (let [stage1-meets (for [a triple b triple] ((inf lat) a b)) - stage1-joins (for [a triple b triple] ((sup lat) a b)) + (let [stage1-meets (set (filter some? (for [a triple b triple] (if (not= a b) ((inf lat) a b))))) + stage1-joins (set (filter some? (for [a triple b triple] (if (not= a b) ((sup lat) a b))))) - stage2-meets (for [a stage1-joins b stage1-joins] ((inf lat) a b)) - stage2-joins (for [a stage1-meets b stage1-meets] ((sup lat) a b)) - - final-meet ((inf lat) ((inf lat) (first stage1-joins) (second stage1-joins)) (last stage1-joins)) - - base-set (set/union stage1-meets - stage1-joins - stage2-meets - stage2-joins - final-meet) - ] - - (make-lattice-nc base-set + stage2-meets (set (filter some? (for [a stage1-joins b stage1-joins] (if (not= a b) ((inf lat) a b))))) + stage2-joins (set (filter some? (for [a stage1-meets b stage1-meets] (if (not= a b) ((sup lat) a b))))) + + + final-meet #{ (into [] ((inf lat) + ((inf lat) (first stage1-joins) (second stage1-joins)) + (last stage1-joins)))} + + base-set (set/union triple + stage1-meets + stage1-joins + stage2-meets + stage2-joins + final-meet)] + + (make-lattice-nc base-set (lattice-order lat) (inf lat) - (sup lat))) -) + (sup lat)) + +)) ;verifies if "concept" is a neutral element in "lat" (defn neutral? [concept lat] (let [base-set (lattice-base-set lat)] - (some identity (for [x base-set y base-set] (distributive? (generate-from-triple [concept x y] lat)))) -)) + (every? identity (for [x base-set y base-set] (distributive? (generate-from-triple [concept x y] lat)))) +) +) ;return all neutral elements in "lat" (defn neutral-concepts [lat] @@ -1638,14 +1643,36 @@ ) ) -;retruns a complement of "concept" in "lat" -(defn complemnt [concept lat] +;retruns all complement of "concept" in "lat" +(defn element-complement [concept lat] (let [base-set (lattice-base-set lat) - top ]) + top (first(filter #(= (second %) #{}) base-set)) + bot (reduce #(if (> (count (second %1)) (count (second %2))) %1 + %2 + ) base-set)] + + (filter #(and (not= % concept) + (= ((sup lat) concept %) top) + (= ((inf lat) concept %) bot)) + base-set)) +) + +;returns a decomposition pair of "lat", if a Libkin decomposition is possible +(defn decomposition [lat] + (let [neutral-element (first (neutral-concepts lat)) + complement (first (element-complement neutral-element lat))] + + [neutral-element complement] +) ) + + + + + ;meets: x-y x-z @@ -1673,10 +1700,14 @@ x-y+x-z+y-z #{"A" "B" "C" "D" "E"} #{[1 "A"] [2 "A"] [2 "B"] [3 "B"] [3 "C"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) (def lat (concept-lattice ctx)) -((inf lat2) [#{1} 0] [#{2} 0]) -(def lat2 (generate-from-triple [[#{5} #{"E" "C" "D"}] [#{4 3} #{"C" "B"}] [#{4 2} #{"B" "A"}]] lat)) +(def ctx2 (make-context #{1 2 3 4 5} + #{"A" "B" "C" "D" "E"} + #{[1 "A"] [2 "A"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) +(def lat2 (concept-lattice ctx)) + + From 2a497abe91ecc5e2418d9c0e5ba59353c6e8a2fe Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 13 Sep 2023 02:26:46 +0200 Subject: [PATCH 085/117] Fully Implemented Libkin Decomposition. --- src/main/clojure/conexp/fca/metrics.clj | 20 +++++++++----------- 1 file changed, 9 insertions(+), 11 deletions(-) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 8ba65e1e0..55b004b59 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -1657,16 +1657,11 @@ base-set)) ) -;returns a decomposition pair of "lat", if a Libkin decomposition is possible -(defn decomposition [lat] - (let [neutral-element (first (neutral-concepts lat)) - complement (first (element-complement neutral-element lat))] - - [neutral-element complement] -) - - -) +;returns all decompositions pair of "lat" for Libkin decompositions +(defn decompositions [lat] + (let [neutral-elements (neutral-concepts lat)] + (for [n neutral-elements c (element-complement n lat)] [n c]) +)) @@ -1708,7 +1703,10 @@ x-y+x-z+y-z (def lat2 (concept-lattice ctx)) - +(def ctx3 (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] + [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] + [7 "A"] [7 "B"] [7 "C"]})) +(def lat3 (concept-lattice ctx3)) From 51371fd2222c646b5713933eae0912ee07a9c255 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 20 Sep 2023 21:07:57 +0200 Subject: [PATCH 086/117] Outsourced Functions. Implemented full Lattice Decomposition. --- .../clojure/conexp/fca/decompositions.clj | 56 ++ src/main/clojure/conexp/fca/metrics.clj | 882 +----------------- 2 files changed, 69 insertions(+), 869 deletions(-) create mode 100644 src/main/clojure/conexp/fca/decompositions.clj diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj new file mode 100644 index 000000000..df76dc144 --- /dev/null +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -0,0 +1,56 @@ +(ns conexp.fca.decompositions + (:require [conexp.base :refer :all] + [conexp.fca + [contexts :refer :all] + [metrics :refer :all] + [lattices :refer :all] + [posets :refer :all]] + )) + + +;returns all decompositions pair of "lat" for Libkin decompositions +(defn libkin-decomposition-pairs [lat] + (let [neutral-elements (neutral-concepts lat)] + (for [n neutral-elements c (element-complement n lat)] [n c]) +)) + + +(defn lattice-ideal [lat concept] + (let [base-set (lattice-base-set lat) + order (lattice-order lat) + new-base-set (filter #(order % concept) base-set)] + + (make-lattice-nc new-base-set + order + (inf lat) + (sup lat)) + +) +) + + +(defn libkin-decomposition-lattices [lat decomp-pair] + [(lattice-ideal lat (first decomp-pair)) + (lattice-ideal lat (last decomp-pair))] +) + + + + +;test +(def ctx (make-context #{1 2 3 4 5} + #{"A" "B" "C" "D" "E"} + #{[1 "A"] [2 "A"] [2 "B"] [3 "B"] [3 "C"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) +(def lat (concept-lattice ctx)) + + +(def ctx2 (make-context #{1 2 3 4 5} + #{"A" "B" "C" "D" "E"} + #{[1 "A"] [2 "A"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) +(def lat2 (concept-lattice ctx)) + + +(def ctx3 (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] + [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] + [7 "A"] [7 "B"] [7 "C"]})) +(def lat3 (concept-lattice ctx3)) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 55b004b59..48de93a31 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -9,6 +9,7 @@ (ns conexp.fca.metrics (:require [clojure.core.reducers :as r] [clojure.math.combinatorics :refer [permuted-combinations combinations]] + [clojure.set :as set] ;; [clojure.math.numeric-tower :refer [log]] [conexp.base :refer :all] [conexp.math.markov :refer :all] @@ -19,821 +20,7 @@ context-object-closure object-derivation random-context objects attributes - context? concept? - diag-context - adiag-context - rand-context]];temp - [exploration :refer :all] - [fast :refer [with-binary-context - to-bitset - bitwise-context-attribute-closure - bitwise-object-derivation - bitwise-attribute-derivation concepts]] - [implications :refer :all] - [lattices :refer [inf sup lattice-base-set make-lattice make-lattice-nc - concept-lattice lattice-order extract-context-from-bv - distributive?]]] - [clojure.set :as set] - [conexp.math.util :refer [eval-polynomial binomial-coefficient]]) - (:import [conexp.fca.lattices Lattice] - [java.util ArrayList BitSet])) - - -;; help (outsource me) -(defn log2 [n] - (/ (Math/log n) (Math/log 2))) - -;;; Concept Stability and the like - -(defn concept-stability - "Compute the concept stability of `concept' in `context'." - [context concept] - - (assert (context? context) - "First argument must be a formal context.") - (assert (and (vector? concept) - (= 2 (count concept)) - (concept? context concept)) - "Second argument must be a formal concept of the given context.") - - (let [[extent intent] [(first concept) (second concept)] - counter (fn counter - ;; Perform depth-first search to count all subsets of - ;; `extent' whose derivation in context yields `intent'. - ;; For this we keep the list `fixed-included' of already - ;; considered elements to be included in the target - ;; subset of `extent', and the list `unfixed' of - ;; unconsidered elements for which it is still to be - ;; decided of whether they will be included or not. - [fixed-included unfixed] - (if (empty? unfixed) - 1 - (let [some-element (first unfixed)] - (+ (counter (conj fixed-included some-element) - (disj unfixed some-element)) - (if (= intent - (object-derivation context - (union fixed-included - (disj unfixed some-element)))) - (counter fixed-included (disj unfixed some-element)) - 0)))))] - (/ (counter #{} extent) - (expt 2 (count extent))))) - -(defn separation-index - "The concept separation is an importance measure for concepts. It - computes the size AxB (c-inc) relative to uncovered incidences Ax(M-B) - and (G-A)xB (o-inc). Max value is 1. - - Klimushkin M., Obiedkov S., Roth C. (2010) Approaches to the - Selection of Relevant Concepts in the Case of Noisy Data. In: Kwuida - L., Sertkaya B. (eds) Formal Concept Analysis. ICFCA 2010. Lecture - Notes in Computer Science, vol 5986. Springer, Berlin, - Heidelberg. https://doi.org/10.1007/978-3-642-11928-6_18" - [context concept] - (assert (context? context) - "First argument must be a formal context.") - (assert (and (vector? concept) - (= 2 (count concept)) - (concept? context concept)) - "Second argument must be a formal concept of the given context.") - (let [[extent intent] concept - c-inc (* (count extent) (count intent)) - g-inc (reduce + - (map - #(count (object-derivation context #{%})) - extent)) - a-inc (reduce + - (map #(count (attribute-derivation context #{%})) - intent)) - o-inc (- (+ g-inc a-inc) - c-inc)] ; is at least c-inc large - (/ c-inc o-inc))) - -(def ^:dynamic *fast-computation* - "Enable computation of concept probability with floating point arithmetic - instead of rationals" - nil) - -(defn concept-probability - "Compute the probability of a `concept' in `context' 𝕂 in the following manner. - Let pₘ be the relative frequence of attribute m in context. The - probability of a subset B ⊆ M in 𝕂 is the product of all pₘ for m ∈ B. - Then the probability of a concept is defined by pr(A,B) := pr(B=B'') - which is ∑_{k=0}^n {n choose k}·p_Bᵏ·(1-p_B)ⁿ⁻ᵏ·∏_{m ∈ M ∖ B}(1-p_mᵏ)." - [context concept] - (let [nr_of_objects (count (objects context)) - n (if *fast-computation* (double nr_of_objects) nr_of_objects) - M (attributes context) - B (second concept) ; intent of concept - P_M_B (mapv #(/ (count (attribute-derivation context #{%})) n ) (difference M B)) - p_B (r/fold * (map #(/ (count (attribute-derivation context #{%})) n) B)) - one_minus_p_B_n (expt (- 1 p_B) n)] - (if (not= (double p_B) 1.0) ;; if concept's extent= n - (loop [k 1 ;; since for k=0 the last term is 0, we can start with 1 - result 0 - binomial n ;; since k=0 the start binomial is n - p_B_k p_B - one_minus_p_B_k (/ one_minus_p_B_n (- 1 p_B)) - P_M_B_k P_M_B ] - (if (or (== k n) (== p_B_k 0)) ;; either done or underflowed probability (double) - result - (let [new_res - (* binomial p_B_k one_minus_p_B_k - (r/fold * (map #(- 1 %) P_M_B_k)))] - (recur - (inc k) - (+ new_res result) - (* binomial (/ (- n k) (inc k))) - (* p_B_k p_B) - (/ one_minus_p_B_k (- 1 p_B)) - (mapv (partial *) P_M_B_k P_M_B))))) - 1))) - - -;;; Robustness of Concepts - -(defn- concept-robustness-add-next-entry - "Helper-function for `concept-robustness-polynomial'. - - This function computes the value e(Y,`concept'), based on the already computed - values e(Z,`concept'), which are given in the second parameter `cache' in the - form [Z, e(Z, `concept')]. - - This function is needed in the algorithm on page 19 in \"Finding Robust - Itemsets under Subsampling\" from Tatti, Moerchen, and Calders." - [concept cache] - (let [newvalue (reduce - (fn [x V] (- x (second V))) - 0 - (filter #(subset? (second (first %)) (second concept)) - cache))] - (conj cache [concept, newvalue]))) - -(defn concept-robustness-polynomial - "Return the coefficients of the robustness polynomial of `concept'. - - For the given `concept' of a context, the coefficients of the polynomial p - corresponding to the robustness is computed by using the seq `concepts' of - all concepts of the context. The optional boolean parameter `sorted?' allows - to declare the seq of concepts as being already sorted by increasing - attribute-set. Thus if v is the result of (robustness-polynomial concept - concepts), then (eval-polynomial v (- 1 alpha)) computes the robustness with - parameter alpha. - - For details see \"Finding Robust Itemsets under Subsampling\" from Tatti, - Moerchen, and Calders, pages 17–19." - ([concept concepts sorted?] - (let [B (second concept) - used-concepts (drop 1 (if sorted? - (filter #(subset? B (second %)) concepts) - (sort-by #(count (second %)) - (filter #(subset? B (second %)) - concepts)))) - ;; store for all subconcepts (C_A,C_B) of concept the vector [C, e(C_B, concept)] - concepts-with-values (reduce - (fn [x y] - (concept-robustness-add-next-entry y x)) - [[concept, 1]] - used-concepts) - sup (count (first concept))] - ;; use the above computed values [C, e(C_B, concept)] to compute the polynomial - (reduce - (fn [old-coefficients entry] - (let [index (- sup (count (first (first entry))))] - (assoc old-coefficients - index (+ (nth old-coefficients index) (second entry))))) - (vec (take (+ 1 sup) (repeat 0))) - concepts-with-values))) - ([concept concepts] - (concept-robustness-polynomial concept concepts false))) - -(defn concept-robustness - "Computes the robustness of a `concept' in a context with parameter `alpha' by - using the seq `concepts' consisting of all concepts of the context. The - optional boolean parameter `sorted?' allows to declare the seq of concepts as - beeing already sorted by increasing size of the attribute set. This function - uses the function concept-robustness-polynomial." - ([concept concepts alpha sorted?] - (assert (and (number? alpha) - (<= 0 alpha 1)) - "Third argument must be between 0 and 1!") - (eval-polynomial (concept-robustness-polynomial concept concepts sorted?) (- 1 alpha))) - ([concept concepts alpha] - (concept-robustness concept concepts alpha false))) - -(defn average-concept-robustness - "Takes the seq `concepts' consisting of all concepts of a context and computes - the average concept robustness with parmater `alpha'." - [concepts alpha] - (assert (and (number? alpha) - (<= 0 alpha 1)) - "Second argument must be between 0 and 1!") - (let [sorted-concepts (sort-by - #(count (second %)) - concepts) - n (count sorted-concepts) - robustness-values (map - #(concept-robustness - (nth sorted-concepts %) - (drop % sorted-concepts) - alpha - true) - (range 0 n))] - (/ (reduce + robustness-values) n))) - - -;;; Similarity Measures for Concepts (implemented by Anselm von Wangenheim) - -(defn jaccard-index - "Computes the Jaccard index of two sets. This is |x ∩ y| / |x ∪ y|. - Returns 1 if both sets are empty." - [x y] - (if (and (empty? x) (empty? y)) - 1 - (/ (count (intersection x y)) (count (union x y))))) - -(defn sorensen-coefficient - "Computes the Sorensen coefficient of two sets. - This is 2 * |x ∩ y| / (|x| + |y|). - Returns 1 if both sets are empty." - [x y] - (if (and (empty? x) (empty? y)) - 1 - (/ (* 2 (count (intersection x y))) (+ (count x) (count y))))) - -(defn weighted-concept-similarity - "Computes a weighted concept similarity for a given similatity measure `sim', - two concepts [`c1' `c2'] and an optional weight `w' (default is 1/2). - - That is the weighted average of the similarity of the extents/object sets - (weight `w') and the intents/attribute sets (weight 1-`w'). - - This is from Alqadah, F. & Bhatnagar, R. (2011), 'Similarity measures in - formal concept analysis.', Ann. Math. Artif. Intell. 61 (3), 249, - https://doi.org/10.1007/s10472-011-9257-7" - ([sim [c1 c2]] (weighted-concept-similarity sim [c1 c2] (/ 1 2))) - ([sim [c1 c2] w] - (assert (and (number? w) - (<= 0 w 1)) - "Thrid argument must be between 0 and 1!") - (+ - (* w (sim (c1 0) (c2 0))) - (* (- 1 w) (sim (c1 1) (c2 1)))))) - - - -;;; Concept stability - -(defn mcs-stability-approximation - "Approximates concept stability with Markov Chains." - [ctx concept sample-size] - (let [counter (atom 0)] - (doall - (for [i (range sample-size)] - (let [prem (first concept) - concl (second concept) - limit (count concl)] - (if (= (attribute-derivation ctx - (take (rand-int limit) - (shuffle concl))) - prem) - (swap! counter inc))))) - (/ @counter sample-size))) - -(defn lds-stability-approximation - "Approximates concept stability with Low-Discrepancy Sampling. The function - takes a context and concept, the sample-size and base (both as integer). - An additional argument may be given to choose the sampling method. - The options are: - :sobol One-dimensional Sobol Sequence (default) - :svdc Scrambled Van der Corput Sequence - - Function based on 'An Efficient Approximation of Concept - Stability Using Low-Discrepancy Sampling' Ibrahim; Missaoui 2018 - https://link.springer.com/chapter/10.1007/978-3-319-91379-7_3 " - ([ctx concept sample-size base] - (lds-stability-approximation ctx concept sample-size base :sobol)) - ([ctx concept sample-size base sampling-method] - (let [lds (atom []) - counter (atom 0) - intent (second concept) - intent-size (count intent) - powerset (subsets intent)] - (doall - (for [i (range sample-size)] - (swap! lds conj (case sampling-method - :sobol (generate-sobol i) - :svdc (generate-svdc i base) - (generate-sobol i))))) - (doall - (for [element @lds] - (let [position (int (+ (* intent-size element) 0.5)) - subset (nth powerset position)] - (if (= (first concept) - (attribute-derivation ctx subset)) - (swap! counter inc))))) - (/ @counter sample-size)))) - -;;; standard lattice properties to some degree - -(defn satisfying-triples - "Given lattice lat, compute triples (a,b,c)∈L³ (pairwise different) - such that they fullfil a given condition. The triples may be - filtered beforehand using prefilter." - ([^Lattice lat condition] - (let [base (into [] (lattice-base-set lat))] - ;; (filter condition (filter prefilter (permuted-combinations base 3))))) - (filter condition (permuted-combinations base 3)))) - ([lat condition prefilter] - (let [base (into [] (lattice-base-set lat))] - (filter condition (filter prefilter (permuted-combinations base 3)))))) - - -(defn distributive-triples - "Given lattice lat, compute triples (x,y,z)∈L³ (pairwise different) - such that they fullfil the distributive property - x∨(y∧z)=(x∨y)∧(x∨z)." - ([^Lattice lat] - (distributive-triples lat (fn [x] true))) - ([^Lattice lat prefilter] - (let [inf (inf lat), - sup (sup lat)] - (satisfying-triples lat (fn [[x y z]] - (= (sup x (inf y z )) - (inf (sup x y) (sup x z)))) - prefilter)))) - -(defn modular-triples - "Given lattice lat, compute triples (x,y,z)∈L³ (pairwire different) - such that they fullfil the modular property x ≤ z ⇒ - x∨(y∧z)=(x∨y)∧z." - ([lat] - (modular-triples lat (fn [x] true))) - ([lat prefilter] - (let [inf (inf lat), - sup (sup lat), - ord (lattice-order lat) - base (into [] (lattice-base-set lat))] - (satisfying-triples lat (fn [[x y z]] - (if (ord x z) ;; if x≤y - (= ;; check x∨(y∧z)=(x∨y)∧z - (sup x (inf y z)) - (inf (sup x y) z)) - true)) - prefilter)))) ;; else always true - -(defn distributivity-degree - "Computes the number of triples (a,b,c)∈L³ (pairwise different) - that fullfil the distributivity law and divides it by the number of - possible pw different triples." - [lat] - (let [n (count (lattice-base-set lat))] - (if (< n 3) - 1 ;; in case we have less than 3 elements we have distributivity - (/ (count (distributive-triples lat)) - (* 6 (binomial-coefficient n 3)))))) - -(defn modularity-degree - "Computes the number of triples (a,b,c)∈L³ (pairwise different) - that fullfil the modularity law and divides it by the number of - possible pw different triples. (tbc later on)" - [lat] - (let [n (count (lattice-base-set lat))] - (if (< n 3) - 1 ;; in case we have less than 3 elements we have modularity - (/ (count (modular-triples lat)) - (* 6 (binomial-coefficient n 3)))))) - -(defn elements-distributivity - "Computes the number of triples (a,b,c)∈L³ (pw different) where either - a=e, b=e, or c=e, that fullfil the modularity law. This number is - then divided it by the number of possible pw different triples of such kind." - [lat e] - (assert (contains? (lattice-base-set lat) e)) - (let [n (count (lattice-base-set lat)), - filterfunc (fn [[x y z]] (or (= x e) (= y e) (= z e)))] - (/ (count (distributive-triples - lat filterfunc)) - (* 6 (binomial-coefficient (- n 1) 2))))) - -(defn elements-modularity - [lat e] - (assert (contains? (lattice-base-set lat) e)) - (let [n (count (lattice-base-set lat))] - (/ (count (modular-triples lat (fn [[x y z]] (or (= x e) (= y e) (= z e))))) - (* 6 (binomial-coefficient (- n 1) 2))))) - -;;; Relevant Attributes (Objects) et Al - -(defn attribute-information-entropy - "Computes the attribute-information-entropy for a given context 𝕂using the formula - (∑_{m ∈ M} 1-{m}''/|M|)/|M|, see https://doi.org/10.1007/978-3-030-23182-8_8" - [ctx] - (let [M (attributes ctx) - nr_of_attributes (count M)] - (/ (- nr_of_attributes - (r/fold + (pmap - (fn [m] (/ (count (context-attribute-closure ctx #{m})) - nr_of_attributes)) - M))) - nr_of_attributes))) - -(defn object-information-entropy - "Computes the object-information-entropy for a given context 𝕂using the formula - (∑_{g ∈ G} 1-{g}''/|G|)/|G|, see https://doi.org/10.1007/978-3-030-23182-8_8" - [ctx] - (attribute-information-entropy (dual-context ctx))) - -(defn information-entropy - "Computes the mean entropy of context ctx based on the equal - weighted sum of attribute-information-entropy and - object-information-entropy." - [ctx] - (/ (+ (attribute-information-entropy ctx) (object-information-entropy ctx)) 2)) - - -(defn shannon-attribute-information-entropy - "Computes the Shannon-attribute-information-entropy for a given context 𝕂using the formula - ∑_{m ∈ M} -{m}''/|M|· log₂ ({m}''/|M|), see https://doi.org/10.1007/978-3-030-23182-8_8" - [ctx] - (let [M (attributes ctx) - nr_of_attributes (count M)] - (r/fold + (pmap (fn [x] (- (* x (log2 x)))) - (pmap - (fn [m] (/ (count (context-attribute-closure ctx #{m})) - nr_of_attributes)) - M))))) - -(defn shannon-object-information-entropy - "Computes the Shannon-object-information-entropy for a given context 𝕂using the formula - ∑_{g ∈ G} -{g}''/|G|· log₂ ({g}''/|G|), see https://doi.org/10.1007/978-3-030-23182-8_8" - [ctx] - (shannon-attribute-information-entropy (dual-context ctx))) - -(defn shannon-attribute-information-entropy-fast - "Computes the Shannon-attribute-information-entropy for a given - context 𝕂using the formula ∑_{m ∈ M} -{m}''/|M|· log₂ ({m}''/|M|), - see https://doi.org/10.1007/978-3-030-23182-8_8. This implementation - resorts to bit vectors in order to increase the computation - speed. This conversion is not adviced for small data sets. " - [ctx] - (with-binary-context ctx - (let [a-closure-counts - (pmap (fn [y] - (let [^BitSet bs (BitSet.)] - (.set bs y) - (bitwise-context-attribute-closure - incidence-matrix - object-count - attribute-count - bs))) - (range attribute-count))] - (- - (r/fold + (map (fn [x] (* (/ (.cardinality ^BitSet x) ^long attribute-count) - (log2 (/ (.cardinality ^BitSet x) ^long attribute-count)))) - a-closure-counts)))))) - - -(defn shannon-object-information-entropy-fast - "Computes the Shannon-object-information-entropy for a given context 𝕂using the formula - ∑_{g ∈ G} -{g}''/|G|· log₂ ({g}''/|G|), see https://doi.org/10.1007/978-3-030-23182-8_8" - [ctx] - (shannon-attribute-information-entropy-fast (dual-context ctx))) - -(defn shannon-information-entropy - "Computes the mean shannon-entropy of context ctx based on the equal - weighted sum of attribute-information-entropy and - object-information-entropy." - [ctx] - (/ (+ (shannon-attribute-information-entropy ctx) - (shannon-object-information-entropy ctx)) 2)) - -(defn shannon-information-entropy-fast - "Computes the mean shannon-entropy of context ctx based on the equal - weighted sum of attribute-information-entropy and - object-information-entropy." - [ctx] - (/ (+ (shannon-attribute-information-entropy-fast ctx) - (shannon-object-information-entropy-fast ctx)) 2)) - -(defn extent-label-function - "Computes the label for given g ∈ G, i.e., the natural number n such - that n=|{c ∈ 𝔅(𝕂) ∣ g ∈ ext(c)}|, see - https://doi.org/10.1007/978-3-030-23182-8_8" - ([ctx g] - (extent-label-function ctx (concepts :in-close ctx) g)) - ([ctx concepts g] - (count - (filter (fn [x] (contains? (first x) g)) - concepts)))) - -(defn intent-label-function - "Computes the label for given m ∈ M, i.e., the natural number n such - that n=|{c ∈ 𝔅(𝕂) ∣ m ∈ int(c)}|, see - https://doi.org/10.1007/978-3-030-23182-8_8" - ([ctx m] - (extent-label-function ctx (concepts :in-close ctx) m)) - ([ctx concepts m] - (count - (filter (fn [x] (contains? (second x) m)) - concepts)))) - -(defn attribute-removal-robust-concepts - "Computes the set of concepts {c ∈ 𝔅(𝕂) ∣ (int(c) ∖ A)' = ext(c)} - for some attribute set A ⊆ M." - ([ctx A] - (attribute-removal-robust-concepts ctx (concepts :in-close ctx) A)) - ([ctx theconcepts A] - (into [] (r/filter (fn [x] (= - (attribute-derivation ctx (difference (second x) A)) - (first x))) - theconcepts)))) - -(defn object-removal-robust-concepts - "Computes the set of concepts {c ∈ 𝔅(𝕂) ∣ (ext(c) ∖ A)' = int(c)} - for some attribute set A ⊆ G." - ([ctx A] - (object-removal-robust-concepts ctx (concepts :in-close ctx) A)) - ([ctx theconcepts A] - (into [] (r/filter (fn [x] (= - (object-derivation ctx (difference (first x) A)) - (second x))) - theconcepts)))) - - -(defn relative-relevance - "Computes for formal context (G,M,I) the relative relevance of - attribute set A ⊆ M, using the formula from Proposition 3.5 in - https://doi.org/10.1007/978-3-030-23182-8_8, i.e., - r(A)=1-∑_{c∈𝔅(𝕂_A)}|ext(c)|/∑_{c∈𝔅(𝕂)}|ext(c)|, - where 𝔅(𝕂_A)={c∈𝔅(𝕂)∣(int(c)∖A)'=ext(c)}" - ([ctx A] - (relative-relevance ctx (concepts :in-close) A)) - ([ctx theconcepts A] - (let [extsum (r/fold + (map (fn [x] (count (first x))) theconcepts))] - (- 1 - (->> theconcepts - (filter - (fn [x] (= (count - (attribute-derivation ctx (difference (second x) A))) - (count (first x))))) - (pmap (fn [x] (count (first x)))) - (r/fold +) - (* (/ 1 extsum))) - )))) - -(defn relative-relevance-fast - "Compute relative-relevance using bitsets" - [ctx theconcepts A] - (with-binary-context ctx - (let [o-prime (partial bitwise-object-derivation incidence-matrix object-count attribute-count) - a-prime (partial bitwise-attribute-derivation incidence-matrix object-count attribute-count) - theextents (pmap (fn [x] (to-bitset object-vector (first x))) theconcepts) - theatts (to-bitset attribute-vector A)] - (- 1 - (/ - (r/fold + (map (fn [x] - (if (= - (let [thing (o-prime x)] - (.andNot thing theatts) ;; remove attribute set - (.cardinality (a-prime thing))) - (.cardinality x)) - (.cardinality x) - 0)) - theextents)) - (r/fold + (map (fn [x] (.cardinality x)) theextents))))))) - -(defn next-maximal-relevant - "Given a formal context (G,M,I), an attribute set A ⊆ M, this - functions computes the most relevant m ∈ M ∖ A with respect to relative-relevance." - ([ctx theconcepts] (next-maximal-relevant ctx theconcepts #{})) - ([ctx theconcepts A] - (let [atts (attributes ctx) - available-atts (difference atts A) - obs (objects ctx)] - (apply max-key (fn [x] (relative-relevance-fast ctx theconcepts (union A #{x}))) - available-atts)))) - -(defn next-n-maximal-relevant - "Based on next-maximal-relevant, compute the the next n maximal - relevant features in a consekutive manner. Please be advised, this - is not necessiraly equivalent to compute the subset N ⊆ M with |N|=n - being the most relevant wrt relative-relevance." - ([ctx theconcepts n] - (next-n-maximal-relevant ctx theconcepts n #{})) - ([ctx theconcepts n A] - (loop [[counter resultset] [0 []]] - (if (< counter n) - (recur [(inc counter) - (conj resultset - (next-maximal-relevant ctx theconcepts (set (union resultset A))))]) - resultset)))) - -(defn n-maximal-relevant - "Based on relative-relevance, compute the the subset N ⊆ M with |N|=n, - such that there is no L ⊆ M with r(N) k n) - result - (recur - (inc k) - (conj result - (let [atts (attributes ctx) - available-atts (difference atts (union A result)) - obs (objects ctx)] - (apply max-key (fn [x] - (let [pctx (make-context obs (union #{x} result A) (incidence ctx))] - (* - (count (concepts :in-close pctx)) - (object-information-entropy pctx)))) - available-atts))))))) - -(defmethod next-n-maximal-relevant-approx :shannon - ([_ ctx n] - (next-n-maximal-relevant-approx :shannon ctx n #{})) - ([_ ctx n A] - (loop [k 1 - result []] - (if (> k n) - result - (recur - (inc k) - (conj result (let [atts (attributes ctx) - available-atts (difference atts (union A result)) - obs (objects ctx)] - (apply max-key (fn [x] - (let [pctx (make-context obs (union #{x} A result) (incidence ctx))] - (* - (count (concepts :in-close pctx)) - (shannon-object-information-entropy-fast pctx)))) - available-atts)))))))) - - -(defn nRandomAtts - [ctx n] - (let [atts (attributes ctx)] - (take n (shuffle atts)))) - -;; (defn rel-consistency ??? -;; "Computes the relative consistency of a subset $N ⊆ M$ with respect to -;; a given formal context (G,M,I), and some attribute subset N ⊆ M" -;; [ctx N] -;; (let [G (objects ctx) -;; M (attributes ctx) -;; MN (difference M N) -;; ctx-N (make-context G N (incidence ctx)) -;; ctx-MN (make-context G MN (incidence ctx))] -;; (let [derive-N (fn [x] (context-object-closure ctx-N x)) -;; derive-MN (fn [x] (context-object-closure ctx-MN x))] -;; (/ -;; (count (filter (fn [x] (subset? (derive-N #{x}) (derive-MN #{x}))) G)) -;; (count G) -;; )))) - -;; ) - - -(defn generate-from-triple [triple lat] - - (let [stage1-meets (for [a triple b triple] (inf lat a b)) - stage1-joins (for [a triple b triple] (sup lat a b)) - - stage2-meets (for [a stage1-joins b stage1-joins] (inf lat a b)) - stage2-joins (for [a stage1-meets b stage1-meets] (sup lat a b)) - - final-meet (inf lat stage1-joins) - - ground-set (set/union stage1-meets - stage1-joins - stage2-meets - stage2-joins - final-meet) - order-function ;tbt - ] -;; Copyright ⓒ the conexp-clj developers; all rights reserved. -;; The use and distribution terms for this software are covered by the -;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) -;; which can be found in the file LICENSE at the root of this distribution. -;; By using this software in any fashion, you are agreeing to be bound by -;; the terms of this license. -;; You must not remove this notice, or any other, from this software. - -(ns conexp.fca.metrics - (:require [clojure.core.reducers :as r] - [clojure.math.combinatorics :refer [permuted-combinations combinations]] - ;; [clojure.math.numeric-tower :refer [log]] - [conexp.base :refer :all] - [conexp.math.markov :refer :all] - [conexp.fca - [contexts :refer [make-context incidence dual-context - attribute-derivation - context-attribute-closure - context-object-closure - object-derivation random-context - objects attributes - context? concept? - adiag-context - rand-context]];temp + context? concept?]] [exploration :refer :all] [fast :refer [with-binary-context to-bitset @@ -841,7 +28,14 @@ bitwise-object-derivation bitwise-attribute-derivation concepts]] [implications :refer :all] - [lattices :refer [inf sup lattice-base-set make-lattice concept-lattice lattice-order]]] + [lattices :refer [inf + sup + lattice-base-set + make-lattice + make-lattice-nc + concept-lattice + lattice-order + distributive?]]] [conexp.math.util :refer [eval-polynomial binomial-coefficient]]) (:import [conexp.fca.lattices Lattice] [java.util ArrayList BitSet])) @@ -1601,7 +795,7 @@ ;; ) ;returns destributive lattice generated by the concepts in "triple" -;tripe must be a collection of three concepts in "lat" +;triple must be a collection of three concepts in "lat" (defn generate-from-triple [triple lat] (let [stage1-meets (set (filter some? (for [a triple b triple] (if (not= a b) ((inf lat) a b))))) @@ -1643,7 +837,7 @@ ) ) -;retruns all complement of "concept" in "lat" +;retruns all complements of "concept" in "lat" (defn element-complement [concept lat] (let [base-set (lattice-base-set lat) top (first(filter #(= (second %) #{}) base-set)) @@ -1657,59 +851,9 @@ base-set)) ) -;returns all decompositions pair of "lat" for Libkin decompositions -(defn decompositions [lat] - (let [neutral-elements (neutral-concepts lat)] - (for [n neutral-elements c (element-complement n lat)] [n c]) -)) - - - - - - -;meets: -x-y -x-z -y-z -x-y-z - -x+y-x+z -x+y-y+z -x+z-y+z - -;joins: -x+y -x+z -y+z -x+y+z - -x-y+x-z -x-y+y-z -x-z+y-z - -x-y+x-z+y-z - -;test -(def ctx (make-context #{1 2 3 4 5} - #{"A" "B" "C" "D" "E"} - #{[1 "A"] [2 "A"] [2 "B"] [3 "B"] [3 "C"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) -(def lat (concept-lattice ctx)) - - -(def ctx2 (make-context #{1 2 3 4 5} - #{"A" "B" "C" "D" "E"} - #{[1 "A"] [2 "A"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) -(def lat2 (concept-lattice ctx)) - - -(def ctx3 (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] - [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] - [7 "A"] [7 "B"] [7 "C"]})) -(def lat3 (concept-lattice ctx3)) ;;; - nil +nil From 5091bb60179c5ad367525c7e47c107327d9d1197 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 21 Sep 2023 18:41:58 +0200 Subject: [PATCH 087/117] Cleanup and Documentation. --- doc/LibkinDecomposition.org | 632 ++++++++++++++++++ .../clojure/conexp/fca/decompositions.clj | 71 +- 2 files changed, 661 insertions(+), 42 deletions(-) create mode 100644 doc/LibkinDecomposition.org diff --git a/doc/LibkinDecomposition.org b/doc/LibkinDecomposition.org new file mode 100644 index 000000000..e3a0e9067 --- /dev/null +++ b/doc/LibkinDecomposition.org @@ -0,0 +1,632 @@ +#+property: header-args :wrap src text +#+property: header-args:text :eval never + +* Libkin Decomposition + +~conexp-clj~ allows for the computation of Libkin Decompositions of lattices. +For an explanation of the concept consult "Direct product decompositions of lattices, closures and relation schemes" by Leonid Libkin + +We will consider the following lattice as an example: + +#+begin_src clojure :exports both +(def ctx (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] + [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] + [7 "A"] [7 "B"] [7 "C"]})) +(def lat (concept-lattice ctx)) +#+end_src + +** Creating Formal Contexts + +~conexp-clj~ lets you easily create formal contexts in a number of ways. We +shall describe some of them in the following. + +A context ~(G,M,I)~ consists of two sets G and M and an incidence realtion I ⊆ +G×M. G is a set of /objects/, M is a set of /attributes/ and ~gIm~ (short for +(g,m) ∈ I) can be read as /g has the attribute m/. To create a context you only +have to define these sets. There a (at least) three options: + +*** Using a defined relation + +The fasted way to construct a formal context is just by writing it down, as in the following example. + +#+begin_src clojure :results silent +(def ctx-1 (make-context [1 2 3] [1 2 3] <=)) +#+end_src + +To see the formal context, just evaluate its variable explicitly + +#+begin_src clojure :exports both +ctx-1 +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 +--+------ +1 |x x x +2 |. x x +3 |. . x + +#+end_src + +*** Defining all sets explicitly + +A formal context can also be specified by directly listing the incidence +relation (using Clojure's own syntax for sets and tuples): + +#+begin_src clojure :exports both +(def ctx-2 (make-context #{1 2 3 4 5 6} + #{1 2 3 4 5 6} + #{[1 1] [1 2] [1 3] [1 5] + [1 6] [2 2] [2 5] [3 3] + [3 6] [4 4] [4 5] [4 6] + [5 5] [6 6]})) +ctx-2 +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 4 5 6 +--+------------ +1 |x x x . x x +2 |. x . . x . +3 |. . x . . x +4 |. . . x x x +5 |. . . . x . +6 |. . . . . x + +#+end_src + +One can enter the cross-table explicitly, using the function +~make-context-from-matrix~, like this + +#+begin_src clojure :exports both +(def ctx-3 (make-context-from-matrix 6 6 + [1 1 1 0 1 1 + 0 1 0 0 1 0 + 0 0 1 0 0 1 + 0 0 0 1 1 1 + 0 0 0 0 1 0 + 0 0 0 0 0 1])) +ctx-3 +#+end_src + +#+RESULTS: +#+begin_src text + |0 1 2 3 4 5 +--+------------ +0 |x x x . x x +1 |. x . . x . +2 |. . x . . x +3 |. . . x x x +4 |. . . . x . +5 |. . . . . x + +#+end_src + +Here, instead of writing out the sets of objects and attributes explicitly, we +have just entered their cardinality ~6~. With this, the set of objects and +attributes automatically gets set to ~#{1 2 3 4 5 6}~. From time to time, this +make save some typing time. + +### Using a custom function + +This will create a formal context with G = M = {1,2,3,4,5,6} and (n,m) in I if +and only if gcd(n,m) = 1: + +#+begin_src clojure :exports both +(def ctx-4 (make-context [1 2 3 4 5 6] + [1 2 3 4 5 6] + (fn [x y] + (= 1 (gcd x y))))) +ctx-4 +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 4 5 6 +--+------------ +1 |x x x x x x +2 |x . x . x . +3 |x x . x x . +4 |x . x . x . +5 |x x x x . x +6 |x . . . x . + +#+end_src + + +*** Creating Random Contexts + +For some experiments it is often helpful to randomly create contexts. Here is +how this can be done in conexp-clj. Of course, the exact result is probably not +the one you see here + +#+begin_src clojure :exports both +(rand-context #{1 2 3} 0.5) +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 +--+------ +1 |x x x +2 |x x . +3 |x . x + +#+end_src + +Here, the first parameter is the set of objects and attributes and the second +parameter is the probality for the incidence. + +** Working with Formal Contexts + +Having created a formal context, there a plenty of possibilities to work with +it. + +*** Basic Accessors + +The most basic operation on formal contexts is to retrieve its components. This +can be done as follows + +#+begin_src clojure :exports both +[(objects ctx-2), (attributes ctx-2), (incidence ctx-2)] +#+end_src + +#+RESULTS: +#+begin_src text +[#{1 4 6 3 2 5} + #{1 4 6 3 2 5} + #{[2 2] [2 5] [3 3] [1 1] [6 6] [4 6] [1 3] [1 5] [5 5] [3 6] [4 5] + [1 6] [4 4] [1 2]}] +#+end_src + +*** Clarifying and Reducing Contexts + +To see if ~ctx-2~ is clarified, you can use the functions ~object-clarified?~, +~attribute-clarified?~, and ~context-clarified?~. + +#+begin_src clojure :exports both +[(object-clarified? ctx-2), + (attribute-clarified? ctx-2), + (context-clarified? ctx-2)] +#+end_src + +#+RESULTS: +#+begin_src text +[true true true] +#+end_src + +If ~ctx-2~ would not be clarified, one could obtain a clarified version of it by +using + +#+begin_src clojure :eval never :exports code +(clarify-attributes ctx-2) +(clarify-objects ctx-2) +(clarify-context ctx-2) +#+end_src + +As another example, for ~ctx-2~, we could for instance compute the arrow +relations (e.g. to see which objects or attributes are irreducible) + +#+begin_src clojure :exports both +[(up-arrows ctx-2), (down-arrows ctx-2)] +#+end_src + +#+RESULTS: +#+begin_src text +[#{[4 3] [6 3] [4 2] [6 5] [5 2] [1 4] [5 6] [2 6] [3 5]} + #{[4 3] [2 3] [4 2] [4 1] [1 4] [3 1] [2 1] [2 6] [3 5] [3 2]}] +#+end_src + +To directly see whether ~ctx-2~ is reduced, use ~context-reduced?~, and to +obtain a reduced version of ~ctx-2~, call ~reduce-context~ like so: + +#+begin_src clojure :exports both +(reduce-context ctx-2) +#+end_src + +#+RESULTS: +#+begin_src text + |2 3 4 5 6 +--+---------- +1 |x x . x x +2 |x . . x . +3 |. x . . x +4 |. . x x x + +#+end_src + +*** Derivation Operations + +Now I want to get all objects, which attribute ~1~ and ~2~ have in common + +#+begin_src clojure :exports both +(attribute-derivation ctx-2 #{1 2}) +#+end_src + +#+RESULTS: +#+begin_src text +#{1} +#+end_src + +The same can be done for sets of objects + +#+begin_src clojure :exports both +(object-derivation ctx-1 #{1 2}) +#+end_src + +#+RESULTS: +#+begin_src text +#{3 2} +#+end_src + +Instead of using this long function names, there are also the abbreviations +~aprime~ and ~oprime~ available. + +If you want to compute the closure of a given set of objects or attributes in +our context use + +#+begin_src clojure :exports both +[ (context-attribute-closure ctx-2 #{1 2}), + (context-object-closure ctx-2 #{1 2}) ] +#+end_src + +#+RESULTS: +#+begin_src text +[#{1 6 3 2 5} #{1 2}] +#+end_src + +*** Formal Concepts and Concept Lattices + +We can compute all intents and extents via + +#+begin_src clojure :exports both +[(extents ctx-2), (intents ctx-2)] +#+end_src + +#+RESULTS: +#+begin_src text +[(#{} + #{4} + #{1} + #{1 4} + #{1 2} + #{1 3} + #{1 4 2 5} + #{1 4 6 3} + #{1 4 6 3 2 5}) + (#{} + #{5} + #{2 5} + #{6} + #{6 5} + #{6 3} + #{4 6 5} + #{1 6 3 2 5} + #{1 4 6 3 2 5})] +#+end_src + +To get all formal concepts use + +#+begin_src clojure :exports both +(concepts ctx-2) +#+end_src + +#+RESULTS: +#+begin_src text +([#{1 4 6 3 2 5} #{}] + [#{1} #{1 6 3 2 5}] + [#{} #{1 4 6 3 2 5}] + [#{4} #{4 6 5}] + [#{1 4 6 3} #{6}] + [#{1 3} #{6 3}] + [#{1 4} #{6 5}] + [#{1 2} #{2 5}] + [#{1 4 2 5} #{5}]) +#+end_src + +If you are only interested in the number of formal concepts, you can instead +just ~count~ the concepts, like so + +#+begin_src clojure :exports both +(count (concepts ctx-2)) +#+end_src + +#+RESULTS: +#+begin_src text +9 +#+end_src + +This can be combined neatly with ~map~ to get the number of concepts for all the +formal contexts we have defined to far + +#+begin_src clojure :exports both +(map (comp count concepts) [ctx-1 ctx-2 ctx-3 ctx-4]) +#+end_src + +#+RESULTS: +#+begin_src text +(3 9 9 8) +#+end_src + +The standard ~comp~ functions implements function composition in Clojure. + +Finally, you can compute the concept lattice using the ~concept-lattice~ +function like so: + +#+begin_src clojure :exports both +(concept-lattice ctx-2) +#+end_src + +#+RESULTS: +#+begin_src text +Lattice on 9 elements. +#+end_src + +Note that this will not give you a picture of the lattice, but a representation +of the algebraic structure. + +*** Canonical Base + +You get the canonical base with (who would have guessed that!) + +user=> (canonical-base ctx-1) +#{(#{b} ==> #{e}) (#{c} ==> #{f}) (#{c f e} ==> #{a b}) + (#{a} ==> #{c b f e}) (#{d} ==> #{f e}) (#{b f e} ==> #{a c})} + +The ~canonical-base~ function can take additional arguments like background +knowledge and filter predicates. See the documentation of this function for +further details: + +#+begin_src clojure :exports both +(doc canonical-base) +#+end_src + +#+RESULTS: +#+begin_src text +------------------------- +conexp.fca.implications/canonical-base +([ctx] [ctx background-knowledge] [ctx background-knowledge predicate]) + Returns the canonical base of given context, as a lazy sequence. Uses + «background-knowledge» as starting set of implications, which will not appear + in the result. If «predicate» is given (a function), computes only those + implications from the canonical base whose premise satisfy this predicate, + i.e. «predicate» returns true on these premises. Note that «predicate» has to + satisfy the same conditions as the predicate to «next-closed-set-in-family». +nil +#+end_src + +*** Further Operations + +There a several further operations you can do with contexts, e.g., the context +apposition, context subposition, and more. For illustration, let us define two +contexts: + +#+begin_src clojure :exports both +(def ctx-5 (make-context #{1 2 3} #{1 2 3} <)) +(def ctx-6 (make-context-from-matrix [1 2 3] + ['a 'b 'c 'd] + [1 1 0 1 + 1 0 1 0 + 0 0 1 1])) +[ctx-5 ctx-6] +#+end_src + +#+RESULTS: +#+begin_src text +[ |1 2 3 +--+------ +1 |. x x +2 |. . x +3 |. . . + |a b c d +--+-------- +1 |x x . x +2 |x . x . +3 |. . x x +] +#+end_src + +The apposition of these two contexts is + +#+begin_src clojure :exports both +(context-apposition ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |[1 0] [2 0] [3 0] [a 1] [b 1] [c 1] [d 1] +--+------------------------------------------ +1 |. x x x x . x +2 |. . x x . x . +3 |. . . . . x x + +#+end_src + +Note how the two sets of attributes are automatically made disjoint by +considering pairs with different second entry. + +Context apposition is a partial operation, as the contexts must have the same +set of objects. The following would not work: + +#+begin_src clojure :exports both +(context-apposition ctx-1 ctx-2) +#+end_src + +#+RESULTS: +#+begin_src text +class java.lang.IllegalArgumentExceptionclass java.lang.IllegalArgumentExceptionIllegalArgumentException Cannot do context apposition, since object sets are not equal. conexp.base/illegal-argument (base.clj:280) +#+end_src + +To compute the dual context, use what you would expect to use: + +#+begin_src clojure :exports both +(dual-context ctx-5) +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 +--+------ +1 |. . . +2 |x . . +3 |x x . + +#+end_src + +Now we can build the subposition of ~ctx-5~ and the dual of ~ctx-6~ + +#+begin_src clojure :exports both +(context-subposition ctx-5 (dual-context ctx-6)) +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 +------+------ +[1 0] |. x x +[2 0] |. . x +[3 0] |. . . +[a 1] |x x . +[b 1] |x . . +[c 1] |. x x +[d 1] |x . x + +#+end_src + +If you want to invert a given context use + +#+begin_src clojure :exports both +(invert-context ctx-5) +#+end_src + +#+RESULTS: +#+begin_src text + |1 2 3 +--+------ +1 |x . . +2 |x x . +3 |x x x + +#+end_src + +You can create a composition of two (suitable) contexts with + +#+begin_src clojure :exports both +(context-composition ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |a b c d +--+-------- +1 |x . x x +2 |. . x x +3 |. . . . + +#+end_src + +The union of two contexts is created by + +#+begin_src clojure :exports both +(context-union ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |a b c d 1 2 3 +--+-------------- +1 |x x . x . x x +2 |x . x . . . x +3 |. . x x . . . + +#+end_src + +Sum to contexts with + +#+begin_src clojure :exports both +(context-sum ctx-5 ctx-6) +#+end_src + +To compute the intersection of two contexts (which is essentially empty), use + +#+begin_src clojure :exports both +(context-intersection ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + | +--+ +1 | +2 | +3 | + +#+end_src + +The context product goes like this + +#+begin_src clojure :exports both +(context-product ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |[1 a] [2 a] [3 a] [1 b] [2 b] [3 b] [1 c] [2 c] [3 c] [1 d] [2 d] [3 d] +------+------------------------------------------------------------------------ +[1 1] |x x x x x x . x x x x x +[2 1] |x x x x x x . . x x x x +[3 1] |x x x x x x . . . x x x +[1 2] |x x x . x x x x x . x x +[2 2] |x x x . . x x x x . . x +[3 2] |x x x . . . x x x . . . +[1 3] |. x x . x x x x x x x x +[2 3] |. . x . . x x x x x x x +[3 3] |. . . . . . x x x x x x + +#+end_src + +If you want to do a context semiproduct + +#+begin_src clojure :exports both +(context-semiproduct ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |[1 0] [2 0] [3 0] [a 1] [b 1] [c 1] [d 1] +------+------------------------------------------ +[1 1] |. x x x x . x +[2 1] |. . x x x . x +[3 1] |. . . x x . x +[1 2] |. x x x . x . +[2 2] |. . x x . x . +[3 2] |. . . x . x . +[1 3] |. x x . . x x +[2 3] |. . x . . x x +[3 3] |. . . . . x x + +#+end_src + +Compute Xia's product + +#+begin_src clojure :exports both +(context-xia-product ctx-5 ctx-6) +#+end_src + +#+RESULTS: +#+begin_src text + |[1 a] [2 a] [3 a] [1 b] [2 b] [3 b] [1 c] [2 c] [3 c] [1 d] [2 d] [3 d] +------+------------------------------------------------------------------------ +[1 1] |. x x . x x x . . . x x +[2 1] |. . x . . x x x . . . x +[3 1] |. . . . . . x x x . . . +[1 2] |. x x x . . . x x x . . +[2 2] |. . x x x . . . x x x . +[3 2] |. . . x x x . . . x x x +[1 3] |x . . x . . . x x . x x +[2 3] |x x . x x . . . x . . x +[3 3] |x x x x x x . . . . . . + +#+end_src diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index df76dc144..73c84c740 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -1,56 +1,43 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + (ns conexp.fca.decompositions (:require [conexp.base :refer :all] + [conexp.math.algebra :refer :all] [conexp.fca [contexts :refer :all] [metrics :refer :all] [lattices :refer :all] - [posets :refer :all]] - )) + [posets :refer :all]])) -;returns all decompositions pair of "lat" for Libkin decompositions -(defn libkin-decomposition-pairs [lat] +(defn libkin-decomposition-pairs + "Returns all decompositions pair of *lat* for Libkin decompositions" + [lat] (let [neutral-elements (neutral-concepts lat)] - (for [n neutral-elements c (element-complement n lat)] [n c]) -)) - - -(defn lattice-ideal [lat concept] - (let [base-set (lattice-base-set lat) - order (lattice-order lat) - new-base-set (filter #(order % concept) base-set)] - - (make-lattice-nc new-base-set - order - (inf lat) - (sup lat)) - -) -) - - -(defn libkin-decomposition-lattices [lat decomp-pair] - [(lattice-ideal lat (first decomp-pair)) - (lattice-ideal lat (last decomp-pair))] -) - - - + (for [n neutral-elements c (element-complement n lat)] [n c]))) -;test -(def ctx (make-context #{1 2 3 4 5} - #{"A" "B" "C" "D" "E"} - #{[1 "A"] [2 "A"] [2 "B"] [3 "B"] [3 "C"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) -(def lat (concept-lattice ctx)) +(defn libkin-decomposition-lattices + "Computes the Lattices Resulting from the Libkin-Decomposition on the + Providen Decomposition Pair." + [lat decomp-pair] + (let [set1 (order-ideal lat (conj #{} (first decomp-pair))) + set2 (order-ideal lat (conj #{} (last decomp-pair))) + order (lattice-order lat)] -(def ctx2 (make-context #{1 2 3 4 5} - #{"A" "B" "C" "D" "E"} - #{[1 "A"] [2 "A"] [4 "A"] [4 "B"] [4 "C"] [5 "C"] [5 "D"] [5 "E"]})) -(def lat2 (concept-lattice ctx)) + [(make-lattice-nc set1 + order + (inf lat) + (sup lat)) + (make-lattice-nc set2 + order + (inf lat) + (sup lat))])) -(def ctx3 (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] - [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] - [7 "A"] [7 "B"] [7 "C"]})) -(def lat3 (concept-lattice ctx3)) From ba3ba7a54929fc7984507ade38c709bae6ca59fb Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 21 Sep 2023 19:07:57 +0200 Subject: [PATCH 088/117] Finished Documentation on Libkin Decomposition. --- doc/LibkinDecomposition.org | 617 +---------------------------- doc/images/cube-lattice.png | Bin 0 -> 68659 bytes doc/images/decomposed-lattice1.png | Bin 0 -> 39343 bytes doc/images/decomposed-lattice2.png | Bin 0 -> 44521 bytes 4 files changed, 16 insertions(+), 601 deletions(-) create mode 100644 doc/images/cube-lattice.png create mode 100644 doc/images/decomposed-lattice1.png create mode 100644 doc/images/decomposed-lattice2.png diff --git a/doc/LibkinDecomposition.org b/doc/LibkinDecomposition.org index e3a0e9067..8c6df8ca5 100644 --- a/doc/LibkinDecomposition.org +++ b/doc/LibkinDecomposition.org @@ -15,618 +15,33 @@ We will consider the following lattice as an example: (def lat (concept-lattice ctx)) #+end_src -** Creating Formal Contexts +[[./images/cube-lattice.png]] -~conexp-clj~ lets you easily create formal contexts in a number of ways. We -shall describe some of them in the following. - -A context ~(G,M,I)~ consists of two sets G and M and an incidence realtion I ⊆ -G×M. G is a set of /objects/, M is a set of /attributes/ and ~gIm~ (short for -(g,m) ∈ I) can be read as /g has the attribute m/. To create a context you only -have to define these sets. There a (at least) three options: - -*** Using a defined relation - -The fasted way to construct a formal context is just by writing it down, as in the following example. - -#+begin_src clojure :results silent -(def ctx-1 (make-context [1 2 3] [1 2 3] <=)) -#+end_src - -To see the formal context, just evaluate its variable explicitly +All decomposition pairs of the lattice can be computed using the method ~libkin-decomposition-pairs~: #+begin_src clojure :exports both -ctx-1 +(def pairs (libkin-decomposition-pairs lat)) #+end_src #+RESULTS: #+begin_src text - |1 2 3 ---+------ -1 |x x x -2 |. x x -3 |. . x - -#+end_src - -*** Defining all sets explicitly - -A formal context can also be specified by directly listing the incidence -relation (using Clojure's own syntax for sets and tuples): - -#+begin_src clojure :exports both -(def ctx-2 (make-context #{1 2 3 4 5 6} - #{1 2 3 4 5 6} - #{[1 1] [1 2] [1 3] [1 5] - [1 6] [2 2] [2 5] [3 3] - [3 6] [4 4] [4 5] [4 6] - [5 5] [6 6]})) -ctx-2 +([[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]] + [[#{7 4 2 5} #{"B"}] [#{7 6} #{"C" "A"}]] + [[#{7 1 4 6} #{"A"}] [#{7 5} #{"C" "B"}]] + [[#{7 5} #{"C" "B"}] [#{7 1 4 6} #{"A"}]] + [[#{7 6 3 5} #{"C"}] [#{7 4} #{"B" "A"}]] + [[#{7 1 4 6 3 2 5} #{}] [#{7} #{"C" "B" "A"}]] + [[#{7} #{"C" "B" "A"}] [#{7 1 4 6 3 2 5} #{}]] + [[#{7 4} #{"B" "A"}] [#{7 6 3 5} #{"C"}]]) #+end_src -#+RESULTS: -#+begin_src text - |1 2 3 4 5 6 ---+------------ -1 |x x x . x x -2 |. x . . x . -3 |. . x . . x -4 |. . . x x x -5 |. . . . x . -6 |. . . . . x - -#+end_src - -One can enter the cross-table explicitly, using the function -~make-context-from-matrix~, like this +The lattices implied by the decomposition through a specific decomposition pair can be exlicitely generated using ~libkin-decomposition-lattices~: #+begin_src clojure :exports both -(def ctx-3 (make-context-from-matrix 6 6 - [1 1 1 0 1 1 - 0 1 0 0 1 0 - 0 0 1 0 0 1 - 0 0 0 1 1 1 - 0 0 0 0 1 0 - 0 0 0 0 0 1])) -ctx-3 +(libkin-decomposition-lattices lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) #+end_src -#+RESULTS: -#+begin_src text - |0 1 2 3 4 5 ---+------------ -0 |x x x . x x -1 |. x . . x . -2 |. . x . . x -3 |. . . x x x -4 |. . . . x . -5 |. . . . . x - -#+end_src - -Here, instead of writing out the sets of objects and attributes explicitly, we -have just entered their cardinality ~6~. With this, the set of objects and -attributes automatically gets set to ~#{1 2 3 4 5 6}~. From time to time, this -make save some typing time. - -### Using a custom function - -This will create a formal context with G = M = {1,2,3,4,5,6} and (n,m) in I if -and only if gcd(n,m) = 1: - -#+begin_src clojure :exports both -(def ctx-4 (make-context [1 2 3 4 5 6] - [1 2 3 4 5 6] - (fn [x y] - (= 1 (gcd x y))))) -ctx-4 -#+end_src - -#+RESULTS: -#+begin_src text - |1 2 3 4 5 6 ---+------------ -1 |x x x x x x -2 |x . x . x . -3 |x x . x x . -4 |x . x . x . -5 |x x x x . x -6 |x . . . x . - -#+end_src - - -*** Creating Random Contexts - -For some experiments it is often helpful to randomly create contexts. Here is -how this can be done in conexp-clj. Of course, the exact result is probably not -the one you see here - -#+begin_src clojure :exports both -(rand-context #{1 2 3} 0.5) -#+end_src - -#+RESULTS: -#+begin_src text - |1 2 3 ---+------ -1 |x x x -2 |x x . -3 |x . x - -#+end_src - -Here, the first parameter is the set of objects and attributes and the second -parameter is the probality for the incidence. - -** Working with Formal Contexts - -Having created a formal context, there a plenty of possibilities to work with -it. - -*** Basic Accessors - -The most basic operation on formal contexts is to retrieve its components. This -can be done as follows - -#+begin_src clojure :exports both -[(objects ctx-2), (attributes ctx-2), (incidence ctx-2)] -#+end_src - -#+RESULTS: -#+begin_src text -[#{1 4 6 3 2 5} - #{1 4 6 3 2 5} - #{[2 2] [2 5] [3 3] [1 1] [6 6] [4 6] [1 3] [1 5] [5 5] [3 6] [4 5] - [1 6] [4 4] [1 2]}] -#+end_src - -*** Clarifying and Reducing Contexts - -To see if ~ctx-2~ is clarified, you can use the functions ~object-clarified?~, -~attribute-clarified?~, and ~context-clarified?~. - -#+begin_src clojure :exports both -[(object-clarified? ctx-2), - (attribute-clarified? ctx-2), - (context-clarified? ctx-2)] -#+end_src - -#+RESULTS: -#+begin_src text -[true true true] -#+end_src - -If ~ctx-2~ would not be clarified, one could obtain a clarified version of it by -using - -#+begin_src clojure :eval never :exports code -(clarify-attributes ctx-2) -(clarify-objects ctx-2) -(clarify-context ctx-2) -#+end_src - -As another example, for ~ctx-2~, we could for instance compute the arrow -relations (e.g. to see which objects or attributes are irreducible) - -#+begin_src clojure :exports both -[(up-arrows ctx-2), (down-arrows ctx-2)] -#+end_src - -#+RESULTS: -#+begin_src text -[#{[4 3] [6 3] [4 2] [6 5] [5 2] [1 4] [5 6] [2 6] [3 5]} - #{[4 3] [2 3] [4 2] [4 1] [1 4] [3 1] [2 1] [2 6] [3 5] [3 2]}] -#+end_src - -To directly see whether ~ctx-2~ is reduced, use ~context-reduced?~, and to -obtain a reduced version of ~ctx-2~, call ~reduce-context~ like so: - -#+begin_src clojure :exports both -(reduce-context ctx-2) -#+end_src - -#+RESULTS: -#+begin_src text - |2 3 4 5 6 ---+---------- -1 |x x . x x -2 |x . . x . -3 |. x . . x -4 |. . x x x - -#+end_src - -*** Derivation Operations - -Now I want to get all objects, which attribute ~1~ and ~2~ have in common - -#+begin_src clojure :exports both -(attribute-derivation ctx-2 #{1 2}) -#+end_src - -#+RESULTS: -#+begin_src text -#{1} -#+end_src - -The same can be done for sets of objects - -#+begin_src clojure :exports both -(object-derivation ctx-1 #{1 2}) -#+end_src - -#+RESULTS: -#+begin_src text -#{3 2} -#+end_src - -Instead of using this long function names, there are also the abbreviations -~aprime~ and ~oprime~ available. - -If you want to compute the closure of a given set of objects or attributes in -our context use - -#+begin_src clojure :exports both -[ (context-attribute-closure ctx-2 #{1 2}), - (context-object-closure ctx-2 #{1 2}) ] -#+end_src - -#+RESULTS: -#+begin_src text -[#{1 6 3 2 5} #{1 2}] -#+end_src - -*** Formal Concepts and Concept Lattices - -We can compute all intents and extents via - -#+begin_src clojure :exports both -[(extents ctx-2), (intents ctx-2)] -#+end_src - -#+RESULTS: -#+begin_src text -[(#{} - #{4} - #{1} - #{1 4} - #{1 2} - #{1 3} - #{1 4 2 5} - #{1 4 6 3} - #{1 4 6 3 2 5}) - (#{} - #{5} - #{2 5} - #{6} - #{6 5} - #{6 3} - #{4 6 5} - #{1 6 3 2 5} - #{1 4 6 3 2 5})] -#+end_src - -To get all formal concepts use - -#+begin_src clojure :exports both -(concepts ctx-2) -#+end_src - -#+RESULTS: -#+begin_src text -([#{1 4 6 3 2 5} #{}] - [#{1} #{1 6 3 2 5}] - [#{} #{1 4 6 3 2 5}] - [#{4} #{4 6 5}] - [#{1 4 6 3} #{6}] - [#{1 3} #{6 3}] - [#{1 4} #{6 5}] - [#{1 2} #{2 5}] - [#{1 4 2 5} #{5}]) -#+end_src - -If you are only interested in the number of formal concepts, you can instead -just ~count~ the concepts, like so - -#+begin_src clojure :exports both -(count (concepts ctx-2)) -#+end_src - -#+RESULTS: -#+begin_src text -9 -#+end_src - -This can be combined neatly with ~map~ to get the number of concepts for all the -formal contexts we have defined to far - -#+begin_src clojure :exports both -(map (comp count concepts) [ctx-1 ctx-2 ctx-3 ctx-4]) -#+end_src +[[./images/decomposed-lattice1.png]] +[[./images/decomposed-lattice2.png]] -#+RESULTS: -#+begin_src text -(3 9 9 8) -#+end_src - -The standard ~comp~ functions implements function composition in Clojure. - -Finally, you can compute the concept lattice using the ~concept-lattice~ -function like so: - -#+begin_src clojure :exports both -(concept-lattice ctx-2) -#+end_src - -#+RESULTS: -#+begin_src text -Lattice on 9 elements. -#+end_src - -Note that this will not give you a picture of the lattice, but a representation -of the algebraic structure. - -*** Canonical Base - -You get the canonical base with (who would have guessed that!) - -user=> (canonical-base ctx-1) -#{(#{b} ==> #{e}) (#{c} ==> #{f}) (#{c f e} ==> #{a b}) - (#{a} ==> #{c b f e}) (#{d} ==> #{f e}) (#{b f e} ==> #{a c})} - -The ~canonical-base~ function can take additional arguments like background -knowledge and filter predicates. See the documentation of this function for -further details: - -#+begin_src clojure :exports both -(doc canonical-base) -#+end_src - -#+RESULTS: -#+begin_src text -------------------------- -conexp.fca.implications/canonical-base -([ctx] [ctx background-knowledge] [ctx background-knowledge predicate]) - Returns the canonical base of given context, as a lazy sequence. Uses - «background-knowledge» as starting set of implications, which will not appear - in the result. If «predicate» is given (a function), computes only those - implications from the canonical base whose premise satisfy this predicate, - i.e. «predicate» returns true on these premises. Note that «predicate» has to - satisfy the same conditions as the predicate to «next-closed-set-in-family». -nil -#+end_src - -*** Further Operations - -There a several further operations you can do with contexts, e.g., the context -apposition, context subposition, and more. For illustration, let us define two -contexts: - -#+begin_src clojure :exports both -(def ctx-5 (make-context #{1 2 3} #{1 2 3} <)) -(def ctx-6 (make-context-from-matrix [1 2 3] - ['a 'b 'c 'd] - [1 1 0 1 - 1 0 1 0 - 0 0 1 1])) -[ctx-5 ctx-6] -#+end_src - -#+RESULTS: -#+begin_src text -[ |1 2 3 ---+------ -1 |. x x -2 |. . x -3 |. . . - |a b c d ---+-------- -1 |x x . x -2 |x . x . -3 |. . x x -] -#+end_src - -The apposition of these two contexts is - -#+begin_src clojure :exports both -(context-apposition ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |[1 0] [2 0] [3 0] [a 1] [b 1] [c 1] [d 1] ---+------------------------------------------ -1 |. x x x x . x -2 |. . x x . x . -3 |. . . . . x x - -#+end_src - -Note how the two sets of attributes are automatically made disjoint by -considering pairs with different second entry. - -Context apposition is a partial operation, as the contexts must have the same -set of objects. The following would not work: - -#+begin_src clojure :exports both -(context-apposition ctx-1 ctx-2) -#+end_src - -#+RESULTS: -#+begin_src text -class java.lang.IllegalArgumentExceptionclass java.lang.IllegalArgumentExceptionIllegalArgumentException Cannot do context apposition, since object sets are not equal. conexp.base/illegal-argument (base.clj:280) -#+end_src - -To compute the dual context, use what you would expect to use: - -#+begin_src clojure :exports both -(dual-context ctx-5) -#+end_src - -#+RESULTS: -#+begin_src text - |1 2 3 ---+------ -1 |. . . -2 |x . . -3 |x x . - -#+end_src - -Now we can build the subposition of ~ctx-5~ and the dual of ~ctx-6~ - -#+begin_src clojure :exports both -(context-subposition ctx-5 (dual-context ctx-6)) -#+end_src - -#+RESULTS: -#+begin_src text - |1 2 3 -------+------ -[1 0] |. x x -[2 0] |. . x -[3 0] |. . . -[a 1] |x x . -[b 1] |x . . -[c 1] |. x x -[d 1] |x . x - -#+end_src - -If you want to invert a given context use - -#+begin_src clojure :exports both -(invert-context ctx-5) -#+end_src - -#+RESULTS: -#+begin_src text - |1 2 3 ---+------ -1 |x . . -2 |x x . -3 |x x x - -#+end_src - -You can create a composition of two (suitable) contexts with - -#+begin_src clojure :exports both -(context-composition ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |a b c d ---+-------- -1 |x . x x -2 |. . x x -3 |. . . . - -#+end_src - -The union of two contexts is created by - -#+begin_src clojure :exports both -(context-union ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |a b c d 1 2 3 ---+-------------- -1 |x x . x . x x -2 |x . x . . . x -3 |. . x x . . . - -#+end_src - -Sum to contexts with - -#+begin_src clojure :exports both -(context-sum ctx-5 ctx-6) -#+end_src - -To compute the intersection of two contexts (which is essentially empty), use - -#+begin_src clojure :exports both -(context-intersection ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - | ---+ -1 | -2 | -3 | - -#+end_src - -The context product goes like this - -#+begin_src clojure :exports both -(context-product ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |[1 a] [2 a] [3 a] [1 b] [2 b] [3 b] [1 c] [2 c] [3 c] [1 d] [2 d] [3 d] -------+------------------------------------------------------------------------ -[1 1] |x x x x x x . x x x x x -[2 1] |x x x x x x . . x x x x -[3 1] |x x x x x x . . . x x x -[1 2] |x x x . x x x x x . x x -[2 2] |x x x . . x x x x . . x -[3 2] |x x x . . . x x x . . . -[1 3] |. x x . x x x x x x x x -[2 3] |. . x . . x x x x x x x -[3 3] |. . . . . . x x x x x x - -#+end_src - -If you want to do a context semiproduct - -#+begin_src clojure :exports both -(context-semiproduct ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |[1 0] [2 0] [3 0] [a 1] [b 1] [c 1] [d 1] -------+------------------------------------------ -[1 1] |. x x x x . x -[2 1] |. . x x x . x -[3 1] |. . . x x . x -[1 2] |. x x x . x . -[2 2] |. . x x . x . -[3 2] |. . . x . x . -[1 3] |. x x . . x x -[2 3] |. . x . . x x -[3 3] |. . . . . x x - -#+end_src - -Compute Xia's product - -#+begin_src clojure :exports both -(context-xia-product ctx-5 ctx-6) -#+end_src - -#+RESULTS: -#+begin_src text - |[1 a] [2 a] [3 a] [1 b] [2 b] [3 b] [1 c] [2 c] [3 c] [1 d] [2 d] [3 d] -------+------------------------------------------------------------------------ -[1 1] |. x x . x x x . . . x x -[2 1] |. . x . . x x x . . . x -[3 1] |. . . . . . x x x . . . -[1 2] |. x x x . . . x x x . . -[2 2] |. . x x x . . . x x x . -[3 2] |. . . x x x . . . x x x -[1 3] |x . . x . . . x x . x x -[2 3] |x x . x x . . . x . . x -[3 3] |x x x x x x . . . . . . - -#+end_src +These lattices may be visualized as described in Concept-Lattices.org . \ No newline at end of file diff --git a/doc/images/cube-lattice.png b/doc/images/cube-lattice.png new file mode 100644 index 0000000000000000000000000000000000000000..7c2ceaab5f064656423944cabe7c80c5144571c2 GIT binary patch literal 68659 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zgU1D%+9K2BrSWTFNhJiRQ*lHLe`S@&^?!@OfOrhC23>F)#8JX34iB!S;j|Qr2U+S(CRQz}a3x w-^rzkOT-;wSlu5#sAP=lyr=MDI4V_l2j$=6U;WsCTDQBlJ8#SR&g Date: Thu, 21 Sep 2023 20:38:58 +0200 Subject: [PATCH 089/117] Added Test for Libkin Decomposition. --- .../clojure/conexp/fca/decompositions.clj | 2 +- .../conexp/fca/decompositions_test.clj | 46 +++++++++++++++++++ 2 files changed, 47 insertions(+), 1 deletion(-) create mode 100644 src/test/clojure/conexp/fca/decompositions_test.clj diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index 73c84c740..fca353a1b 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -25,7 +25,7 @@ (defn libkin-decomposition-lattices "Computes the Lattices Resulting from the Libkin-Decomposition on the - Providen Decomposition Pair." + Provided Decomposition Pair." [lat decomp-pair] (let [set1 (order-ideal lat (conj #{} (first decomp-pair))) set2 (order-ideal lat (conj #{} (last decomp-pair))) diff --git a/src/test/clojure/conexp/fca/decompositions_test.clj b/src/test/clojure/conexp/fca/decompositions_test.clj new file mode 100644 index 000000000..822489e9b --- /dev/null +++ b/src/test/clojure/conexp/fca/decompositions_test.clj @@ -0,0 +1,46 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.decompositions-test + (:require [conexp.base :refer :all] + [conexp.math.algebra :refer :all] + [conexp.fca + [contexts :refer :all] + [metrics :refer :all] + [lattices :refer :all] + [posets :refer :all] + [decompositions :refer :all]]) + (:use clojure.test)) + + +(deftest test-libkin + (let [ctx (make-context #{1 2 3 4 5 6 7} + #{"A" "B" "C"} + #{[1 "A"] [2 "B"] [3 "C"] + [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] + [7 "A"] [7 "B"] [7 "C"]}) + cube-lat (concept-lattice ctx) + cube-lat-decomp-pairs (seq [[[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]] + [[#{7 4 2 5} #{"B"}] [#{7 6} #{"C" "A"}]] + [[#{7 1 4 6} #{"A"}] [#{7 5} #{"C" "B"}]] + [[#{7 5} #{"C" "B"}] [#{7 1 4 6} #{"A"}]] + [[#{7 6 3 5} #{"C"}] [#{7 4} #{"B" "A"}]] + [[#{7 1 4 6 3 2 5} #{}] [#{7} #{"C" "B" "A"}]] + [[#{7} #{"C" "B" "A"}] [#{7 1 4 6 3 2 5} #{}]] + [[#{7 4} #{"B" "A"}] [#{7 6 3 5} #{"C"}]]]) + decomp-ctx1 (make-context #{6 7} + #{"A" "B" "C"} + #{[6 "A"] [6 "C"] [7 "A"] [7 "B"] [7 "C"]}) + decomp-lat1 (concept-lattice decomp-ctx1) + decomp-ctx2 (make-context #{2 4 5 7} + #{"A" "B" "C"} + #{[2 "B"] [4 "A"] [4 "B"] [5 "B"] [5 "C"] [7 "A"] [7 "B"] [7 "C"]}) + decomp-lat2 (concept-lattice decomp-ctx2)] + + (is (= (libkin-decomposition-pairs cube-lat) cube-lat-decomp-pairs)) + (is (= (libkin-decomposition-lattices cube-lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) [decomp-lat1 decomp-lat2])))) From e4412cd558841c43bfa340cb1bd8a487a061268a Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Tue, 26 Sep 2023 22:08:06 +0200 Subject: [PATCH 090/117] Implemented Poset Product. --- src/main/clojure/conexp/fca/posets.clj | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/src/main/clojure/conexp/fca/posets.clj b/src/main/clojure/conexp/fca/posets.clj index c93be4897..026da28ee 100644 --- a/src/main/clojure/conexp/fca/posets.clj +++ b/src/main/clojure/conexp/fca/posets.clj @@ -9,7 +9,8 @@ (ns conexp.fca.posets (:require [conexp.base :refer :all] [conexp.math.algebra :refer :all] - [conexp.fca.contexts :refer :all])) + [conexp.fca.contexts :refer :all] + [clojure.math.combinatorics :refer [cartesian-product]])) (deftype Poset [base-set order-function] Object @@ -161,3 +162,10 @@ (recur (union filter #{next-element}) (union upper-neighbours (poset-upper-neighbours poset next-element)) (first (difference upper-neighbours filter)))))) + +(defn poset-product + [a b] + (make-poset (cartesian-product (base-set a) (base-set b)) + (fn [x y] (and ((order a) (first x) (first y)) + ((order b) (last x) (last y))))) +) From b80578dc2a45d9c7acd89b8dc2e99e66d297c5e1 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 27 Sep 2023 17:13:39 +0200 Subject: [PATCH 091/117] Implemented Product Functions for Posets and Lattices. Improved Tests and Documentation. --- doc/LibkinDecomposition.org | 11 ++- doc/images/cube-lattice.png | Bin 68659 -> 79656 bytes doc/images/decomposed-lattice1.png | Bin 39343 -> 43363 bytes doc/images/decomposed-lattice2.png | Bin 44521 -> 47096 bytes doc/images/prod-lattice.png | Bin 0 -> 96875 bytes src/main/clojure/conexp/fca/lattices.clj | 9 ++- .../conexp/fca/decompositions_test.clj | 68 +++++++++++++----- 7 files changed, 68 insertions(+), 20 deletions(-) create mode 100644 doc/images/prod-lattice.png diff --git a/doc/LibkinDecomposition.org b/doc/LibkinDecomposition.org index 8c6df8ca5..b72bc1df5 100644 --- a/doc/LibkinDecomposition.org +++ b/doc/LibkinDecomposition.org @@ -17,6 +17,9 @@ We will consider the following lattice as an example: [[./images/cube-lattice.png]] +A Libkin decomposition of a lattice L is a pair of sublattices of L, whose product is isomorphic to L. +Libkin decompositions are each induced by a decomposition pair, a neutral element in L and its Complement. + All decomposition pairs of the lattice can be computed using the method ~libkin-decomposition-pairs~: #+begin_src clojure :exports both @@ -35,13 +38,19 @@ All decomposition pairs of the lattice can be computed using the method ~libkin- [[#{7 4} #{"B" "A"}] [#{7 6 3 5} #{"C"}]]) #+end_src +Computing the order ideal of both entries of the pair yields the two sublattices forming the decomposition. + The lattices implied by the decomposition through a specific decomposition pair can be exlicitely generated using ~libkin-decomposition-lattices~: #+begin_src clojure :exports both (libkin-decomposition-lattices lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) #+end_src +These lattices may be visualized as described in Concept-Lattices.org . + [[./images/decomposed-lattice1.png]] [[./images/decomposed-lattice2.png]] -These lattices may be visualized as described in Concept-Lattices.org . \ No newline at end of file +The product of these lattices yields a lattice isomorphic to L: + 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Datastructure @@ -460,6 +461,12 @@ (let [B+D (intersection B D)] [(attribute-derivation ctx B+D) B+D])))))) +(defn lattice-product + [a b] + (make-lattice (cartesian-product (base-set a) (base-set b)) + (fn [x y] (and ((order a) (first x) (first y)) + ((order b) (last x) (last y)))))) + ;;; nil diff --git a/src/test/clojure/conexp/fca/decompositions_test.clj b/src/test/clojure/conexp/fca/decompositions_test.clj index 822489e9b..19f8900df 100644 --- a/src/test/clojure/conexp/fca/decompositions_test.clj +++ b/src/test/clojure/conexp/fca/decompositions_test.clj @@ -17,30 +17,62 @@ [decompositions :refer :all]]) (:use clojure.test)) - -(deftest test-libkin - (let [ctx (make-context #{1 2 3 4 5 6 7} +;cube context +(def ctx1 (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] - [7 "A"] [7 "B"] [7 "C"]}) - cube-lat (concept-lattice ctx) - cube-lat-decomp-pairs (seq [[[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]] + [7 "A"] [7 "B"] [7 "C"]})) +(def lat1 (concept-lattice ctx1)) + +(def decomp-pairs1 (seq [[[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]] [[#{7 4 2 5} #{"B"}] [#{7 6} #{"C" "A"}]] [[#{7 1 4 6} #{"A"}] [#{7 5} #{"C" "B"}]] [[#{7 5} #{"C" "B"}] [#{7 1 4 6} #{"A"}]] [[#{7 6 3 5} #{"C"}] [#{7 4} #{"B" "A"}]] [[#{7 1 4 6 3 2 5} #{}] [#{7} #{"C" "B" "A"}]] [[#{7} #{"C" "B" "A"}] [#{7 1 4 6 3 2 5} #{}]] - [[#{7 4} #{"B" "A"}] [#{7 6 3 5} #{"C"}]]]) - decomp-ctx1 (make-context #{6 7} - #{"A" "B" "C"} - #{[6 "A"] [6 "C"] [7 "A"] [7 "B"] [7 "C"]}) - decomp-lat1 (concept-lattice decomp-ctx1) - decomp-ctx2 (make-context #{2 4 5 7} - #{"A" "B" "C"} - #{[2 "B"] [4 "A"] [4 "B"] [5 "B"] [5 "C"] [7 "A"] [7 "B"] [7 "C"]}) - decomp-lat2 (concept-lattice decomp-ctx2)] - - (is (= (libkin-decomposition-pairs cube-lat) cube-lat-decomp-pairs)) - (is (= (libkin-decomposition-lattices cube-lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) [decomp-lat1 decomp-lat2])))) + [[#{7 4} #{"B" "A"}] [#{7 6 3 5} #{"C"}]]])) +(def ctx1-decomp-1 (concept-lattice (make-context #{6 7} + #{"A" "B" "C"} + #{[6 "A"] [6 "C"] [7 "A"] [7 "B"] [7 "C"]}))) +(def ctx1-decomp-2 (concept-lattice (make-context #{2 4 5 7} + #{"A" "B" "C"} + #{[2 "B"] [4 "A"] [4 "B"] [5 "B"] [5 "C"] [7 "A"] [7 "B"] [7 "C"]}))) + +;no libkin decompositions +(def ctx2 (make-context #{1 2 3 4 5} + #{1 2 3 4 5} + #{[1 2] [1 3] [1 5] + [2 3] + [3 1] [3 2] [3 3] [3 4] + [4 3] [4 4] + [5 3] [5 5]})) +(def lat2 (concept-lattice ctx2)) + +;only decomposable by top and bot +(def ctx3 (make-context #{1 2 3 4 5 6} + #{1 2 3 4 5 6} + #{[1 1] [1 4] [1 5] + [2 1] [2 5] [2 6] + [3 2] [3 6] + [4 1] [4 5] + [5 2] [5 4] + [6 2] [6 3] [6 4] [6 5]})) +(def lat3 (concept-lattice ctx3)) +(def decomp-pairs3 (seq [[[#{} #{1 4 6 3 2 5}] [#{1 4 6 3 2 5} #{}]] + [[#{1 4 6 3 2 5} #{}] [#{} #{1 4 6 3 2 5}]]])) + + +(deftest test-libkin + + (is (= (libkin-decomposition-pairs lat1) + decomp-pairs1)) + (is (= (libkin-decomposition-lattices lat1 [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) + [ctx1-decomp-1 ctx1-decomp-2])) + + (is (empty? (libkin-decomposition-pairs lat2))) + + (is (= (libkin-decomposition-pairs lat3) + decomp-pairs3)) +) From b9a9b05762b7eaac8953a8a3ceafdbdb922680f3 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 28 Sep 2023 16:57:56 +0200 Subject: [PATCH 092/117] Added Libkin Decomposition Documentation to Index. --- README.md | 1 + 1 file changed, 1 insertion(+) diff --git a/README.md b/README.md index f5925b81a..429ef1b7b 100644 --- a/README.md +++ b/README.md @@ -32,6 +32,7 @@ much more. 8. [Computing Traces in Contexts](doc/code/trace-context.clj) 9. [Counting Quasiorders](doc/code/quasiorders.clj) 10. [Rudolph's Algorithm for Computing Bases](doc/code/rudolph_computation.clj) + 11. [Libkin Decompositions](doc/LibkinDecomposition.org) 5. Advanced Topics 1. [pq-cores](doc/pq-cores-in-Formal-Contexts.md) 2. [REST-API Usage](doc/REST-API-usage.md) From 37f8bdbf5063cf0d8637451e0e5663dead5ed32b Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 4 Oct 2023 20:09:31 +0200 Subject: [PATCH 093/117] Improved Documentation. --- doc/LibkinDecomposition.org | 9 +++++++-- doc/images/car-lattice.png | Bin 0 -> 531171 bytes doc/images/decomposed-lattice1.png | Bin 43363 -> 217120 bytes doc/images/decomposed-lattice2.png | Bin 47096 -> 101493 bytes 4 files changed, 7 insertions(+), 2 deletions(-) create mode 100644 doc/images/car-lattice.png diff --git a/doc/LibkinDecomposition.org b/doc/LibkinDecomposition.org index b72bc1df5..a361d21cd 100644 --- a/doc/LibkinDecomposition.org +++ b/doc/LibkinDecomposition.org @@ -15,7 +15,7 @@ We will consider the following lattice as an example: (def lat (concept-lattice ctx)) #+end_src -[[./images/cube-lattice.png]] +[[./images/car-lattice.png]] A Libkin decomposition of a lattice L is a pair of sublattices of L, whose product is isomorphic to L. Libkin decompositions are each induced by a decomposition pair, a neutral element in L and its Complement. @@ -43,11 +43,16 @@ Computing the order ideal of both entries of the pair yields the two sublattices The lattices implied by the decomposition through a specific decomposition pair can be exlicitely generated using ~libkin-decomposition-lattices~: #+begin_src clojure :exports both -(libkin-decomposition-lattices lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) +(def lattice-pair (libkin-decomposition-lattices lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]])) #+end_src These lattices may be visualized as described in Concept-Lattices.org . +#+begin_src text +(draw-lattice (first lattice-pair)) +(draw-lattice (last lattice-pair)) +#+end_src + [[./images/decomposed-lattice1.png]] [[./images/decomposed-lattice2.png]] diff --git a/doc/images/car-lattice.png b/doc/images/car-lattice.png new file mode 100644 index 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z>v=icVkfd~4Wnk=g*|CRVzVOEB25jaszl2$2sx;#$*72E^v7SE3UDxRKl09OPL=HN zf6H`LQDg@9W#id1*`k*{^*vtHSCT23$xkg9?jF36lw-S*k~R?wLVE(B8x;Z+h%zgH015bhGKgd;JH4G?csJw~7ww3S8h;52#>o#cf za8p*K8~KqmlK`8S*a~)yLe{-bFH>A)bo-NkP*iylFVBRMQLHxFV9{1@segzQ>@TRX zIvaANJ08~>Im%6R{u+0U5E=t}3KyhP%~4)j!w| zr~?7r`&MrHXCvvu|q?sJNI!0o%GH8IxG4b z87E+-4k!>aMjj68{?)FTL+zQ#+4Yusv|5x+?qF2RFzRM3H>Qc=-%@w=_~p6PPAb=o zw-{~mKf+&0J@~w;KmV%1begbs$kAED;sJ$sv?!%jEj8}zv)@xm4nb9#IyKT*DipB+3^K~MhggzMmB;2Rc_VckJw~>&S^!Immn__FI;d!IB<^sWi v+=CqFJ&E-CHVPk)p>FoygJX<|7WQiW`tjm<-eL3%eC&wnPpSX0`}O|=ITuoV From 977fcbda1bde8ddc4ba69240102d03497d4341a5 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Sat, 28 Oct 2023 20:08:27 +0200 Subject: [PATCH 094/117] Fixed Imlementation of Complement Computation. --- src/main/clojure/conexp/fca/metrics.clj | 19 +++++++++++-------- .../conexp/fca/decompositions_test.clj | 6 +++++- 2 files changed, 16 insertions(+), 9 deletions(-) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 48de93a31..03192e6ab 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -837,23 +837,26 @@ ) ) +(defn top-element [lat] + (reduce #((sup lat) %1 %2) (lattice-base-set lat)) +) + +(defn bot-element [lat] + (reduce #((inf lat) %1 %2) (lattice-base-set lat)) +) + ;retruns all complements of "concept" in "lat" (defn element-complement [concept lat] - (let [base-set (lattice-base-set lat) - top (first(filter #(= (second %) #{}) base-set)) - bot (reduce #(if (> (count (second %1)) (count (second %2))) %1 - %2 - ) base-set)] + (let [base-set (lattice-base-set lat)] (filter #(and (not= % concept) - (= ((sup lat) concept %) top) - (= ((inf lat) concept %) bot)) + (= ((sup lat) concept %) (top-element lat)) + (= ((inf lat) concept %) (bot-element lat))) base-set)) ) - ;;; nil diff --git a/src/test/clojure/conexp/fca/decompositions_test.clj b/src/test/clojure/conexp/fca/decompositions_test.clj index 19f8900df..ff5cd7e84 100644 --- a/src/test/clojure/conexp/fca/decompositions_test.clj +++ b/src/test/clojure/conexp/fca/decompositions_test.clj @@ -50,6 +50,9 @@ [5 3] [5 5]})) (def lat2 (concept-lattice ctx2)) +(def decomp-pairs-2 (seq [[[#{1 4 3 2 5} #{3}] [#{} #{1 4 3 2 5}]] + [[#{} #{1 4 3 2 5}] [#{1 4 3 2 5} #{3}]]])) + ;only decomposable by top and bot (def ctx3 (make-context #{1 2 3 4 5 6} #{1 2 3 4 5 6} @@ -71,7 +74,8 @@ (is (= (libkin-decomposition-lattices lat1 [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) [ctx1-decomp-1 ctx1-decomp-2])) - (is (empty? 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From df1a5b62e2b2ffc221ad1f32f03c4b15d99fc3f3 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 2 Nov 2023 22:01:49 +0100 Subject: [PATCH 096/117] Removed Redundant Functions. --- src/main/clojure/conexp/fca/metrics.clj | 18 +++++------------- 1 file changed, 5 insertions(+), 13 deletions(-) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 03192e6ab..a47b8fcb8 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -35,7 +35,9 @@ make-lattice-nc concept-lattice lattice-order - distributive?]]] + distributive? + lattice-one + lattice-zero]]] [conexp.math.util :refer [eval-polynomial binomial-coefficient]]) (:import [conexp.fca.lattices Lattice] [java.util ArrayList BitSet])) @@ -837,26 +839,16 @@ ) ) -(defn top-element [lat] - (reduce #((sup lat) %1 %2) (lattice-base-set lat)) -) - -(defn bot-element [lat] - (reduce #((inf lat) %1 %2) (lattice-base-set lat)) -) ;retruns all complements of "concept" in "lat" (defn element-complement [concept lat] (let [base-set (lattice-base-set lat)] (filter #(and (not= % concept) - (= ((sup lat) concept %) (top-element lat)) - (= ((inf lat) concept %) (bot-element lat))) + (= ((sup lat) concept %) (lattice-one lat)) + (= ((inf lat) concept %) (lattice-zero lat))) base-set)) ) - - - ;;; nil From 60b5f0dedd40b32af711a1048736a4c39db7fdd6 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Fri, 3 Nov 2023 00:32:10 +0100 Subject: [PATCH 097/117] Added Decompositions Namespace to Documentation. --- doc/LibkinDecomposition.org | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/doc/LibkinDecomposition.org b/doc/LibkinDecomposition.org index a361d21cd..9c78994b1 100644 --- a/doc/LibkinDecomposition.org +++ b/doc/LibkinDecomposition.org @@ -6,6 +6,15 @@ ~conexp-clj~ allows for the computation of Libkin Decompositions of lattices. For an explanation of the concept consult "Direct product decompositions of lattices, closures and relation schemes" by Leonid Libkin +Some of the following functions require the ~decompositions~ namespace: + + +#+begin_src clojure +(use 'conexp.fca.decompositions) +#+end_src + +(use 'conexp.fca.decompositions) + We will consider the following lattice as an example: #+begin_src clojure :exports both From 80966f88a5f6a90912769f04db1294fea6082dea Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Tue, 27 Feb 2024 14:55:12 +0100 Subject: [PATCH 098/117] New test statements --- .../clojure/conexp/fca/decompositions.clj | 22 ++++++++++++++++++- 1 file changed, 21 insertions(+), 1 deletion(-) diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index c9beb89ed..fd1471987 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -114,9 +114,29 @@ "wood-properties-d.ctx" "zoo-d.ctx"}) - +(defn list-all-decomps [ctx-list] + (for [ctx ctx-list + pair (libkin-decomposition-pairs (concept-lattice (read-context ctx)))] + (println (str ctx ": " (libkin-decomposition-lattices (concept-lattice (read-context ctx)) pair))))) ;(use 'conexp.io.contexts) ;(def ctx (read-context "testing-data/Bird-Diet.ctx")) ;(make-context #{} #{} (incidence ctx)) ;(write-context :burmeister (distributive-exploration (read-context "testing-data/Bird-Diet.ctx") ectx) "ird-diet-d.ctx") + +(def ctx (read-context "drive_concepts_for_motorcars-d.ctx")) + +(def drive-objs #{"All-wheel" "Conventional" "Front-wheel" "Mid-engine" "Rear-wheel"}) + +(def drive-attrs #{"C-h" "C-l" "C-vl" "De+" "De++" "Dl+" + "Dl++" "Dl-" "E+" "E++" "E-" "E--" + "M-" "M--" "R+" "R++" "S-n" "S-u/n"}) + +(def drive-ctx (make-context drive-objs drive-attrs (incidence ctx))) + + +(def drive-ctx1 (make-context drive-objs #{"C-h" "C-l"} (incidence ctx))) + +(def drive-ctx2 (make-context drive-objs #{"C-vl" "De+" "De++" "Dl+" + "Dl++" "Dl-" "E+" "E++" "E-" "E--" + "M-" "M--" "R+" "R++" "S-n" "S-u/n"} (incidence ctx))) From 646e9e903a45451350db1a397a46afad79a60214 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Fri, 1 Mar 2024 18:21:36 +0100 Subject: [PATCH 099/117] Corrected Implementation for Computing Neutral Elements. --- .../clojure/conexp/fca/decompositions.clj | 17 +++++++++++++++++ src/main/clojure/conexp/fca/metrics.clj | 19 +++++++++++++++---- 2 files changed, 32 insertions(+), 4 deletions(-) diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index fd1471987..2e574118e 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -114,6 +114,23 @@ "wood-properties-d.ctx" "zoo-d.ctx"}) +(def ctx-list2 #{"testing-data/Animals.ctx" + "testing-data/Bird-Diet.ctx" + "testing-data/Brunson-Club.ctx" + "testing-data/Forum-Romanum.ctx" + "testing-data/Living-Beings-and-Water.ctx" + "testing-data/Southern-Woman.ctx" + "testing-data/Wood-Properties.ctx" + "testing-data/bodiesofwater.cxt" + "testing-data/digits.cxt" + "testing-data/drive_concepts_for_motorcars.cxt" + "testing-data/living_beings_and_water.cxt" + "testing-data/myctx.cxt" + "testing-data/testcontext.cxt" + "testing-data/triangles.cxt" + "testing-data/california.ctx" +}) + (defn list-all-decomps [ctx-list] (for [ctx ctx-list pair (libkin-decomposition-pairs (concept-lattice (read-context ctx)))] diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index a47b8fcb8..bd2de3619 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -796,8 +796,7 @@ ;; ) -;returns destributive lattice generated by the concepts in "triple" -;triple must be a collection of three concepts in "lat" +;INCORRECT (defn generate-from-triple [triple lat] (let [stage1-meets (set (filter some? (for [a triple b triple] (if (not= a b) ((inf lat) a b))))) @@ -825,13 +824,25 @@ )) -;verifies if "concept" is a neutral element in "lat" -(defn neutral? [concept lat] +;incorrect +(defn neutral?_incorrect [concept lat] + (println "alt") (let [base-set (lattice-base-set lat)] (every? identity (for [x base-set y base-set] (distributive? (generate-from-triple [concept x y] lat)))) ) ) +(defn neutral? [a lat] + (let [base-set (lattice-base-set lat) + join (sup lat) + meet (inf lat)] + (every? identity (for [x base-set y base-set] (= (meet (meet (join a x) (join a y)) (join x y)) + (join (join (meet a x) (meet a y)) (meet x y))))) +) +) + + + ;return all neutral elements in "lat" (defn neutral-concepts [lat] (let [base-set (lattice-base-set lat)] From 6bbbdef335d667e01705b07d5b1f382feef1b591 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Mon, 22 Jan 2024 22:40:12 +0100 Subject: [PATCH 100/117] Documentation Correction. --- doc/LibkinDecomposition.org | 41 +++++++++++++++++++++++++----------- doc/images/prod-lattice.png | Bin 96875 -> 412450 bytes 2 files changed, 29 insertions(+), 12 deletions(-) diff --git a/doc/LibkinDecomposition.org b/doc/LibkinDecomposition.org index 9c78994b1..6c1c12a67 100644 --- a/doc/LibkinDecomposition.org +++ b/doc/LibkinDecomposition.org @@ -18,9 +18,7 @@ Some of the following functions require the ~decompositions~ namespace: We will consider the following lattice as an example: #+begin_src clojure :exports both -(def ctx (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} #{[1 "A"] [2 "B"] [3 "C"] - [4 "A"] [4 "B"] [5 "B"] [5 "C"] [6 "A"] [6 "C"] - [7 "A"] [7 "B"] [7 "C"]})) +(def ctx (read-context "testing-data/drive_concepts_for_motorcars.cxt")) (def lat (concept-lattice ctx)) #+end_src @@ -37,14 +35,26 @@ All decomposition pairs of the lattice can be computed using the method ~libkin- #+RESULTS: #+begin_src text -([[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]] - [[#{7 4 2 5} #{"B"}] [#{7 6} #{"C" "A"}]] - [[#{7 1 4 6} #{"A"}] [#{7 5} #{"C" "B"}]] - [[#{7 5} #{"C" "B"}] [#{7 1 4 6} #{"A"}]] - [[#{7 6 3 5} #{"C"}] [#{7 4} #{"B" "A"}]] - [[#{7 1 4 6 3 2 5} #{}] [#{7} #{"C" "B" "A"}]] - [[#{7} #{"C" "B" "A"}] [#{7 1 4 6 3 2 5} #{}]] - [[#{7 4} #{"B" "A"}] [#{7 6 3 5} #{"C"}]]) +([[#{"Conventional" "All-wheel" "Rear-wheel" "Mid-engine"} #{"Dl+"}] + [#{"Front-wheel"} + #{"E+" "C-l" "De+" "C-vl" "E++" "Dl-" "S-u" "R+" "M+" "R++"}]] + [[#{} + #{"E+" "C-l" "E-" "C-h" "De+" "Dl+" "C-vl" "E++" "S-u/n" "Dl++" + "Dl-" "M++" "S-u" "R+" "S-n" "S-o" "De-" "De++" "M+" "M--" "R--" + "C-m" "M-" "R++" "E--"}] + [#{"Conventional" "All-wheel" "Rear-wheel" "Mid-engine" + "Front-wheel"} + #{}]] + [[#{"Conventional" "All-wheel" "Rear-wheel" "Mid-engine" + "Front-wheel"} + #{}] + [#{} + #{"E+" "C-l" "E-" "C-h" "De+" "Dl+" "C-vl" "E++" "S-u/n" "Dl++" + "Dl-" "M++" "S-u" "R+" "S-n" "S-o" "De-" "De++" "M+" "M--" "R--" + "C-m" "M-" "R++" "E--"}]] + [[#{"Front-wheel"} + #{"E+" "C-l" "De+" "C-vl" "E++" "Dl-" "S-u" "R+" "M+" "R++"}] + [#{"Conventional" "All-wheel" "Rear-wheel" "Mid-engine"} #{"Dl+"}]]) #+end_src Computing the order ideal of both entries of the pair yields the two sublattices forming the decomposition. @@ -52,7 +62,9 @@ Computing the order ideal of both entries of the pair yields the two sublattices The lattices implied by the decomposition through a specific decomposition pair can be exlicitely generated using ~libkin-decomposition-lattices~: #+begin_src clojure :exports both -(def lattice-pair (libkin-decomposition-lattices lat [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]])) +(def lattice-pair (libkin-decomposition-lattices lat [[#{"Conventional" "All-wheel" "Rear-wheel" "Mid-engine"} #{"Dl+"}] + [#{"Front-wheel"} + #{"E+" "C-l" "De+" "C-vl" "E++" "Dl-" "S-u" "R+" "M+" "R++"}]])) #+end_src These lattices may be visualized as described in Concept-Lattices.org . @@ -65,6 +77,11 @@ These lattices may be visualized as described in Concept-Lattices.org . 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[concept lat] - (let [base-set (lattice-base-set lat)] - (every? identity (for [x base-set y base-set] (distributive? (generate-from-triple [concept x y] lat)))) +(defn neutral? [a lat] + "Verifies if *a* is a neutral element in *lat*." + (let [base-set (lattice-base-set lat) + join (sup lat) + meet (inf lat)] + (every? identity (for [x base-set y base-set] (= (meet (meet (join a x) (join a y)) (join x y)) + (join (join (meet a x) (meet a y)) (meet x y))))) ) ) -;return all neutral elements in "lat" (defn neutral-concepts [lat] + "Returns all neutral elements in *lat*." (let [base-set (lattice-base-set lat)] (filter #(neutral? % lat) base-set) ) ) -;retruns all complements of "concept" in "lat" (defn element-complement [concept lat] + "Returns all complements of *concept* in *lat*." (let [base-set (lattice-base-set lat)] (filter #(and (not= % concept) From 32c421f5e18aacc6d1f473b191d09885f2e3d4bc Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 7 Mar 2024 15:22:47 +0100 Subject: [PATCH 102/117] Removed Unneeded Function. --- src/main/clojure/conexp/fca/metrics.clj | 28 ------------------------- 1 file changed, 28 deletions(-) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index a57f35fc4..1b9858f87 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -796,34 +796,6 @@ ;; ) -;returns destributive lattice generated by the concepts in "triple" -;triple must be a collection of three concepts in "lat" -(defn generate-from-triple [triple lat] - - (let [stage1-meets (set (filter some? (for [a triple b triple] (if (not= a b) ((inf lat) a b))))) - stage1-joins (set (filter some? (for [a triple b triple] (if (not= a b) ((sup lat) a b))))) - - stage2-meets (set (filter some? (for [a stage1-joins b stage1-joins] (if (not= a b) ((inf lat) a b))))) - stage2-joins (set (filter some? (for [a stage1-meets b stage1-meets] (if (not= a b) ((sup lat) a b))))) - - - final-meet #{ (into [] ((inf lat) - ((inf lat) (first stage1-joins) (second stage1-joins)) - (last stage1-joins)))} - - base-set (set/union triple - stage1-meets - stage1-joins - stage2-meets - stage2-joins - final-meet)] - - (make-lattice-nc base-set - (lattice-order lat) - (inf lat) - (sup lat)) - -)) (defn neutral? [a lat] "Verifies if *a* is a neutral element in *lat*." From d7d3c75c5b91d35b3abbf1ae5972bd9ae836b9d4 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Wed, 27 Mar 2024 15:20:37 +0100 Subject: [PATCH 103/117] Methods for completing a lattice to a distributive lattice --- .../clojure/conexp/fca/distributivity.clj | 173 ++++++++++++++++++ 1 file changed, 173 insertions(+) create mode 100644 src/main/clojure/conexp/fca/distributivity.clj diff --git a/src/main/clojure/conexp/fca/distributivity.clj b/src/main/clojure/conexp/fca/distributivity.clj new file mode 100644 index 000000000..108c7c51a --- /dev/null +++ b/src/main/clojure/conexp/fca/distributivity.clj @@ -0,0 +1,173 @@ +;; Copyright ⓒ the conexp-clj developers; all rights reserved. +;; The use and distribution terms for this software are covered by the +;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) +;; which can be found in the file LICENSE at the root of this distribution. +;; By using this software in any fashion, you are agreeing to be bound by +;; the terms of this license. +;; You must not remove this notice, or any other, from this software. + +(ns conexp.fca.distributivity + "Methods to complete a lattice or context to the a distributive + lattice." + (:require [conexp.base :refer :all] + [conexp.fca.contexts :refer :all] + [conexp.fca.implications :refer :all])) + +(defn birkhoff-downset-completion + "Returns the downset birkhoff completion of a formal context. + (G,M,I) -> (G,M U J(G),I U {(g1,g2) in G x J(G) | not g1''>= g2'' })." + [ctx] + (let [irreducible-objects (-> ctx reduce-objects objects)] + (assert (empty? (intersection (attributes ctx) irreducible-objects)) "Object and Attribute sets should be disjoint") + (make-context (objects ctx) + (union (attributes ctx) irreducible-objects) + (union (incidence-relation ctx) + (set-of [g1 g2] [g1 (objects ctx), g2 irreducible-objects + :when + (not (subset? (context-object-closure ctx #{g2}) + (context-object-closure ctx #{g1})))]) )) )) + +(defn birkhoff-upset-completion + "Returns the downset birkhoff completion of a formal context. + (G,M,I) -> (G U M(M), M,I U {(m1,m2) in M x M(M) | not m1''>= m2'' })." + [ctx] + (-> ctx dual-context birkhoff-downset-completion dual-context)) + + +(defmulti non-distributive-proper-premises + "Returns the set of proper premises that contradict the distributivity property." + (fn [thing _] thing)) + +(defmethod non-distributive-proper-premises :attributes + [_ ctx] + (assert (context-reduced? ctx) "The context must be reduced") + (filter (fn [A] (<= 2 (count A))) + (proper-premises ctx)) ) + + +(defmethod non-distributive-proper-premises :objects + [_ ctx] + (->> ctx dual-context + (non-distributive-proper-premises :attributes)) ) + + +(defmulti proper-premise-height + "Returns the number of super-concepts of the premise." + (fn [thing _ _] thing)) + +(defmethod proper-premise-height :objects + [_ ctx premise] + (assert (context-reduced? ctx) "The context must be reduced") + (let [exts (extents ctx)] + (->> exts + (filter #(subset? premise %1)) + count) )) + +(defmethod proper-premise-height :attributes + [_ ctx premise] + (assert (context-reduced? ctx) "The context must be reduced") + (let [ints (intents ctx)] + (->> ints + (filter #(subset? premise %1)) + count) )) + +(defmulti proper-premise-support + "Returns the number of super-concepts of the premise." + (fn [thing _ _] thing)) + +(defmethod proper-premise-support :objects + [_ ctx premise] + (assert (context-reduced? ctx) "The context must be reduced") + (support premise (dual-context ctx)) ) + +(defmethod proper-premise-support :attributes + [_ ctx premise] + (assert (context-reduced? ctx) "The context must be reduced") + (support premise (dual-context ctx)) ) + + +(defmulti truncated-birkhoff-downset-completion + (fn [ctx order amount] order)) + +(defmethod truncated-birkhoff-downset-completion :height + [ctx _ amount] + (truncated-birkhoff-downset-completion ctx + (fn [proper-premise] (proper-premise-height :objects ctx proper-premise)) + amount) ) + +(defmethod truncated-birkhoff-downset-completion :support + [ctx _ amount] + (truncated-birkhoff-downset-completion ctx + (fn [proper-premise] (proper-premise-support :objects ctx proper-premise)) + amount) ) + +(defmethod truncated-birkhoff-downset-completion :default + [ctx order-fn amount] + (assert (context-reduced? ctx) "The context must be reduced") + (let [premises (-> ctx dual-context proper-premises ) + non-distributive (filter (fn [A] (not= 1 (count A))) + premises) + removed (->> non-distributive + (sort-by order-fn > ) + (take amount)) + truncated-premise-set (difference (set premises) + (set removed)) + truncated-implication-set (map (fn [premise] (make-implication premise + (context-object-closure ctx premise))) + truncated-premise-set) + truncated-closure-system (->> truncated-implication-set + clop-by-implications + (all-closed-sets (objects ctx))) + unreduced-completion (make-context (objects ctx) + truncated-closure-system + (fn [g m] (contains? m g)))] + (make-context (objects ctx) + (union (attributes ctx) + (-> unreduced-completion reduce-context attributes)) + (union (incidence-relation ctx) + (incidence-relation unreduced-completion))) )) + +(defn truncated-birkhoff-upset-completion + [ctx order-fn amount] + (-> ctx dual-context + (truncated-birkhoff-downset-completion order-fn amount) + dual-context) ) + +(defn truncated-birkhoff-upset-comption-by-implications + [ctx imps & {:keys [clarify] :or {clarify false}}] + (let [L (->> imps clop-by-implications (all-closed-sets (attributes ctx))) + JL (-> L (make-context (attributes ctx) contains?) + reduce-objects) + ctxJL (make-context (into (objects ctx) (objects JL)) + (attributes ctx) + (into (incidence-relation ctx) + (incidence-relation JL))) + clarify-JL (filter (fn [o] (if (coll? o) + (not (some (fn [g] (= (object-derivation ctx #{g}) + (object-derivation JL #{o}))) + (objects ctx))) + true)) (objects ctxJL))] + (if clarify + (make-context clarify-JL + (attributes ctxJL) + (incidence-relation ctxJL)) + ctxJL ) ) ) + +(defn truncated-birkhoff-downset-comption-by-implications + [ctx imps & args] + (-> ctx dual-context + (truncated-birkhoff-upset-comption-by-implications imps args) + dual-context) ) + +(defn truncated-birkhoff-upset-completion + [ctx] + (let [P (proper-premise-implications ctx) + truncated-imps (filter (fn [i] (let [p (premise i)] + (or (= 1 (count p)) + (= (attributes ctx) (context-attribute-closure ctx p))))) + P)] + (truncated-birkhoff-upset-comption-by-implications ctx truncated-imps) ) ) + +(defn truncated-birkhoff-downset-completion + [ctx] + (-> ctx dual-context truncated-birkhoff-upset-completion dual-context) ) From 8d4635e92d376693656571dc230a2c7b10efb47b Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Mon, 13 May 2024 16:00:07 +0200 Subject: [PATCH 104/117] Added Combinatorial Product --- .../clojure/conexp/fca/decompositions.clj | 45 ++++++++++++++++++- 1 file changed, 43 insertions(+), 2 deletions(-) diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index 2e574118e..a6dccece5 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -14,7 +14,8 @@ [contexts :refer :all] [metrics :refer :all] [lattices :refer :all] - [posets :refer :all]])) + [posets :refer :all]] + [clojure.set :as set])) (defn libkin-decomposition-pairs @@ -42,6 +43,35 @@ (inf lat) (sup lat))])) +(defn combinatorial-decomposition-lattices + "Computes the Lattices Resulting from the Libkin-Decomposition on the + Provided Decomposition Pair." + [lat decomp-pair] + (let [set1 (order-filter lat (conj #{} (first decomp-pair))) + set2 (order-filter lat (conj #{} (last decomp-pair))) + order (lattice-order lat)] + + + [(make-lattice-nc set1 + order + (inf lat) + (sup lat)) + (make-lattice-nc set2 + order + (inf lat) + (sup lat))])) + +(defn combinatorial-product [a b] + + (let [con1 (base-set a) + con2 (base-set b) + new-base-set (for [x con1 y con2] + [(set/intersection (first x) (first y)) + (set/union (second x) (second y))])] + + (make-lattice new-base-set #(subset? (first %1) (first %2)))) +) + (defn add-obj [ctx obj incidence] "Returns a new context with obj added." (make-context (union (objects ctx) #{obj}) (attributes ctx) incidence)) @@ -89,7 +119,18 @@ (for [ctx ctx-list] (println (concept-lattice (read-context ctx)))) -(def pair-list (for [ctx ctx-list] (libkin-decomposition-pairs (concept-lattice (read-context ctx))))) +(def pair-list (for [ctx ctx-list] (libkin-decomposition-pairs (concept-lattice (reduce-context (read-context ctx)))))) + +(defn check-combinatorial-decomps [ctx-list] + (for [ctx ctx-list] + (let [lat (concept-lattice (reduce-context (read-context ctx))) + decomposition-pairs (libkin-decomposition-pairs lat)] + (for [pair decomposition-pairs] + (let [decomp (combinatorial-decomposition-lattices lat pair)] + (println (str ctx ": " (= (combinatorial-product (first decomp) (second decomp)) lat)))) + +)))) + (def ctx-list #{"animals-d.ctx" "bird-diet-d.ctx" From 76a8da04a2e95df10121d70a3c1f77437d4cb549 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Fri, 7 Jun 2024 00:56:21 +0200 Subject: [PATCH 105/117] Added Experimental Functions and Testing Data. --- .../clojure/conexp/fca/decompositions.clj | 104 +++++++++++++++++- 1 file changed, 103 insertions(+), 1 deletion(-) diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index a6dccece5..50fa07cb5 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -9,6 +9,7 @@ (ns conexp.fca.decompositions (:require [conexp.base :refer :all] [conexp.math.algebra :refer :all] + [conexp.gui.draw :refer :all] [conexp.io.contexts :refer :all] [conexp.fca [contexts :refer :all] @@ -18,6 +19,20 @@ [clojure.set :as set])) +(defn context-from-lattice [lat] + (let [concepts (base-set lat) + unions (reduce #(vector (set/union (first %1) (first %2)) (set/union (second %1) (second %2))) concepts) + objects (first unions) + attributes (second unions) + incidence (for [c concepts obj (first c) attr (second c)] [obj attr])] + (make-context objects attributes incidence) + ) + +) + + + + (defn libkin-decomposition-pairs "Returns all decompositions pair of *lat* for Libkin decompositions" [lat] @@ -68,10 +83,74 @@ new-base-set (for [x con1 y con2] [(set/intersection (first x) (first y)) (set/union (second x) (second y))])] - (make-lattice new-base-set #(subset? (first %1) (first %2)))) ) + +(defn hierarchy [lat] + (let [pairs (libkin-decomposition-pairs lat) + sublats (set (flatten (for [p pairs] (combinatorial-decomposition-lattices lat p))))] + (make-lattice sublats #(subset? (base-set %1) (base-set %2)))) +) + +(defn attr-union [ctx1 ctx2] + "ctx1 and ctx2 must have the same set of objects" + (if (not (= (objects ctx1) (objects ctx2))) + (println "Contexts do not have the same objects!") + (make-context (objects ctx1) + (set/union (attributes ctx1) (attributes ctx2)) + (set/union (incidence ctx1) (incidence ctx2)))) + +) + +(defn attr-intersection [ctx1 ctx2] + "ctx1 and ctx2 must have the same set of objects" + (if (not (= (objects ctx1) (objects ctx2))) + (println "Contexts do not have the same objects!") + (make-context (objects ctx1) + (set/intersection (attributes ctx1) (attributes ctx2)) + (set/intersection (incidence ctx1) (incidence ctx2)))) + +) + +(defn ctx-hierarchy [lat] + (let [pairs (libkin-decomposition-pairs lat) + sublats (set (flatten (for [p pairs] (combinatorial-decomposition-lattices lat p)))) + subctxs (map context-from-lattice sublats)] + + (make-lattice subctxs attr-intersection attr-union)) +) + +(defn test-hierarchy [lat] + (let [hlat (hierarchy lat) + base (base-set hlat) + join (sup hlat) + meet (inf hlat)] + (for [lat1 base lat2 base] (if (and (= (join lat1 lat2) + (concept-lattice (attr-union (context-from-lattice lat1) + (context-from-lattice lat2)))) + (= (meet lat1 lat2) + (concept-lattice (attr-intersection (context-from-lattice lat1) + (context-from-lattice lat2))))) + (println "TRUE") + (do (println "FALSE") + (println (context-from-lattice lat)) + (println (context-from-lattice lat1)) + (println (context-from-lattice lat2)) + ))) +)) + +(defn test-combi-decomp [lat] + (let [pairs (libkin-decomposition-pairs lat)] + (for [pair pairs] (if (= (combinatorial-product (first (combinatorial-decomposition-lattices lat pair)) + (second (combinatorial-decomposition-lattices lat pair))) + lat) + (println "TRUE") + (println "FALSE"))) +) +) + + (defn add-obj [ctx obj incidence] "Returns a new context with obj added." (make-context (union (objects ctx) #{obj}) (attributes ctx) incidence)) @@ -198,3 +277,26 @@ (def drive-ctx2 (make-context drive-objs #{"C-vl" "De+" "De++" "Dl+" "Dl++" "Dl-" "E+" "E++" "E-" "E--" "M-" "M--" "R+" "R++" "S-n" "S-u/n"} (incidence ctx))) + + + +(def ctx (make-context #{1 2 3 4} #{"A" "B" "C" "D"} #{[1 "A"] [1 "D"] + [2 "B"] [2 "D"] + [3 "C"] [3 "D"] + [4 "A"] [4 "B"] [4 "C"]})) + +(def diamond (make-context #{1 2 3 4} #{"A" "B" "C"} #{[1 "A"] + [2 "B"] + [3 "C"] + [4 "A"] [4 "B"] [4 "C"]})) + +(def chain (make-context #{1 2 3 4} #{"E"} #{[1 "E"] [2 "E"] [3 "E"]})) + +(def bigctx (make-context #{1 2 3 4 5} #{"A" "B" "C" "D" "E"} #{[1 "A"] [1 "D"] [1 "E"] + [2 "B"] [2 "D"] [2 "E"] + [3 "C"] [3 "D"] [3 "E"] + [4 "A"] [4 "B"] [4 "C"] [4 "D"] + [5 "A"] [5 "B"] [5 "C"] [5 "E"]})) + +(def testctx (make-context #{1 2 3} #{"A" "B"} #{[1 "A"] [2 "B"]})) +(def testctx2 (make-context #{1 2 3} #{"C"} #{})) From 3c922895cb52298839bc6e3e6b7260b312693684 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Fri, 7 Jun 2024 12:46:18 +0200 Subject: [PATCH 106/117] Cleanup for Verification Functions. --- .../clojure/conexp/fca/decompositions.clj | 134 ++++++------------ 1 file changed, 40 insertions(+), 94 deletions(-) diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index 50fa07cb5..7602bf95b 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -20,35 +20,29 @@ (defn context-from-lattice [lat] + "Computes the underlying context of a lattice by reading the incidence of all objects." + "Does not work with the *lattice-product* method." (let [concepts (base-set lat) - unions (reduce #(vector (set/union (first %1) (first %2)) (set/union (second %1) (second %2))) concepts) + unions (reduce #(vector (set/union (first %1) (first %2)) (set/union (second %1) (second %2))) concepts) objects (first unions) attributes (second unions) incidence (for [c concepts obj (first c) attr (second c)] [obj attr])] (make-context objects attributes incidence) - ) + )) -) - - - - -(defn libkin-decomposition-pairs +(defn libkin-decomposition-pairs [lat] "Returns all decompositions pair of *lat* for Libkin decompositions" - [lat] (let [neutral-elements (neutral-concepts lat)] (for [n neutral-elements c (element-complement n lat)] [n c]))) -(defn libkin-decomposition-lattices +(defn libkin-decomposition-lattices [lat decomp-pair] "Computes the Lattices Resulting from the Libkin-Decomposition on the Provided Decomposition Pair." - [lat decomp-pair] (let [set1 (order-ideal lat (conj #{} (first decomp-pair))) set2 (order-ideal lat (conj #{} (last decomp-pair))) order (lattice-order lat)] - [(make-lattice-nc set1 order (inf lat) @@ -58,15 +52,13 @@ (inf lat) (sup lat))])) -(defn combinatorial-decomposition-lattices +(defn combinatorial-decomposition-lattices [lat decomp-pair] "Computes the Lattices Resulting from the Libkin-Decomposition on the Provided Decomposition Pair." - [lat decomp-pair] (let [set1 (order-filter lat (conj #{} (first decomp-pair))) set2 (order-filter lat (conj #{} (last decomp-pair))) order (lattice-order lat)] - [(make-lattice-nc set1 order (inf lat) @@ -77,7 +69,8 @@ (sup lat))])) (defn combinatorial-product [a b] - + "Computes the combinatoial produce of two lattices. + May fail if *a* and *b* are not complemented neutral ideals of the same lattice" (let [con1 (base-set a) con2 (base-set b) new-base-set (for [x con1 y con2] @@ -88,13 +81,15 @@ (defn hierarchy [lat] + "Computes the hierarchy lattice of all combinatorial decompositions." (let [pairs (libkin-decomposition-pairs lat) sublats (set (flatten (for [p pairs] (combinatorial-decomposition-lattices lat p))))] (make-lattice sublats #(subset? (base-set %1) (base-set %2)))) ) (defn attr-union [ctx1 ctx2] - "ctx1 and ctx2 must have the same set of objects" + "Unifies the attributes of *ctx1* and *ctx2*. + *ctx1* and *ctx2* must have the same objects." (if (not (= (objects ctx1) (objects ctx2))) (println "Contexts do not have the same objects!") (make-context (objects ctx1) @@ -104,7 +99,8 @@ ) (defn attr-intersection [ctx1 ctx2] - "ctx1 and ctx2 must have the same set of objects" + "Intersects the attributes of *ctx1* and *ctx2*. + *ctx1* and *ctx2* must have the same objects." (if (not (= (objects ctx1) (objects ctx2))) (println "Contexts do not have the same objects!") (make-context (objects ctx1) @@ -114,6 +110,7 @@ ) (defn ctx-hierarchy [lat] + "Computes the hierarchy lattice of the contexts of all combinatoiral decompositions." (let [pairs (libkin-decomposition-pairs lat) sublats (set (flatten (for [p pairs] (combinatorial-decomposition-lattices lat p)))) subctxs (map context-from-lattice sublats)] @@ -122,18 +119,20 @@ ) (defn test-hierarchy [lat] + "Verifies whether all meets and joins in the hierarchy lattice can be represented by attribute-union + and attribute-intersection." (let [hlat (hierarchy lat) base (base-set hlat) join (sup hlat) meet (inf hlat)] (for [lat1 base lat2 base] (if (and (= (join lat1 lat2) (concept-lattice (attr-union (context-from-lattice lat1) - (context-from-lattice lat2)))) + (context-from-lattice lat2)))) (= (meet lat1 lat2) (concept-lattice (attr-intersection (context-from-lattice lat1) - (context-from-lattice lat2))))) - (println "TRUE") - (do (println "FALSE") + (context-from-lattice lat2))))) + :OK + (do (println "FALSE##################################") (println (context-from-lattice lat)) (println (context-from-lattice lat1)) (println (context-from-lattice lat2)) @@ -141,66 +140,29 @@ )) (defn test-combi-decomp [lat] + "Verifies whether all combinatorial decompositions of *lat* are reversed by the combinatorial product." (let [pairs (libkin-decomposition-pairs lat)] (for [pair pairs] (if (= (combinatorial-product (first (combinatorial-decomposition-lattices lat pair)) (second (combinatorial-decomposition-lattices lat pair))) lat) - (println "TRUE") - (println "FALSE"))) -) -) + :OK + (println "FALSE#####################################"))) +)) (defn add-obj [ctx obj incidence] - "Returns a new context with obj added." + "Returns a new context with *obj* added." (make-context (union (objects ctx) #{obj}) (attributes ctx) incidence)) (defn add-attr [ctx attr incidence] + "Returns a new context with *attr* added." (make-context (objects ctx) (union (attributes ctx) #{attr}) incidence)) -(defn distributive-exploration [ctx empty-ctx] - (let [objs (objects ctx) - attr (attributes ctx) - incidence (incidence ctx) - start empty-ctx] - - (loop [subctx start - rest-objs objs - rest-attr attr - object-next true] - -(println (count (objects subctx))) - - (let [new-obj (first (filter #(distributive? (concept-lattice (add-obj subctx % incidence))) rest-objs)) - new-attr (first (filter #(distributive? (concept-lattice (add-attr subctx % incidence))) rest-attr))] - - (if (not (or new-obj new-attr)) - subctx - (if (and object-next new-obj) - (recur (add-obj subctx new-obj incidence) - (difference rest-objs #{new-obj}) - rest-attr - false) - (if (and (not object-next) new-attr) - (recur (add-attr subctx new-attr incidence) - rest-objs - (difference rest-attr #{new-attr}) - true) - (recur subctx - rest-objs - rest-attr - (not object-next))))) - ) - ))) - -(for [ctx ctx-list] (println (concept-lattice (read-context ctx)))) - -(def pair-list (for [ctx ctx-list] (libkin-decomposition-pairs (concept-lattice (reduce-context (read-context ctx)))))) - (defn check-combinatorial-decomps [ctx-list] + "Checks whether all combinatorial decompositions of the contexts in *ctx-list* are reversed by the combinatorial product." (for [ctx ctx-list] (let [lat (concept-lattice (reduce-context (read-context ctx))) decomposition-pairs (libkin-decomposition-pairs lat)] @@ -211,6 +173,17 @@ )))) +(defn test-cycle [number] + (loop [counter number] + (let [ctx (reduce-attributes (random-context #{1 2 3 4 5} #{"A" "B" "C" "D" "E"} 0.5)) + lat (concept-lattice ctx)] + + (doall (test-hierarchy lat)) + (doall (test-combi-decomp lat)) + (if (not (= counter 0)) + (recur (- counter 1)))))) + + (def ctx-list #{"animals-d.ctx" "bird-diet-d.ctx" "bodiesofwater-d.ctx" @@ -251,34 +224,6 @@ "testing-data/california.ctx" }) -(defn list-all-decomps [ctx-list] - (for [ctx ctx-list - pair (libkin-decomposition-pairs (concept-lattice (read-context ctx)))] - (println (str ctx ": " (libkin-decomposition-lattices (concept-lattice (read-context ctx)) pair))))) - -;(use 'conexp.io.contexts) -;(def ctx (read-context "testing-data/Bird-Diet.ctx")) -;(make-context #{} #{} (incidence ctx)) -;(write-context :burmeister (distributive-exploration (read-context "testing-data/Bird-Diet.ctx") ectx) "ird-diet-d.ctx") - -(def ctx (read-context "drive_concepts_for_motorcars-d.ctx")) - -(def drive-objs #{"All-wheel" "Conventional" "Front-wheel" "Mid-engine" "Rear-wheel"}) - -(def drive-attrs #{"C-h" "C-l" "C-vl" "De+" "De++" "Dl+" - "Dl++" "Dl-" "E+" "E++" "E-" "E--" - "M-" "M--" "R+" "R++" "S-n" "S-u/n"}) - -(def drive-ctx (make-context drive-objs drive-attrs (incidence ctx))) - - -(def drive-ctx1 (make-context drive-objs #{"C-h" "C-l"} (incidence ctx))) - -(def drive-ctx2 (make-context drive-objs #{"C-vl" "De+" "De++" "Dl+" - "Dl++" "Dl-" "E+" "E++" "E-" "E--" - "M-" "M--" "R+" "R++" "S-n" "S-u/n"} (incidence ctx))) - - (def ctx (make-context #{1 2 3 4} #{"A" "B" "C" "D"} #{[1 "A"] [1 "D"] [2 "B"] [2 "D"] @@ -299,4 +244,5 @@ [5 "A"] [5 "B"] [5 "C"] [5 "E"]})) (def testctx (make-context #{1 2 3} #{"A" "B"} #{[1 "A"] [2 "B"]})) + (def testctx2 (make-context #{1 2 3} #{"C"} #{})) From eeecb4a6d72fb5340dc54df7fa65678c09510108 Mon Sep 17 00:00:00 2001 From: Johannes Hirth Date: Thu, 13 Jun 2024 09:36:35 +0200 Subject: [PATCH 107/117] fixed boring imports --- src/main/clojure/conexp/fca/distributivity.clj | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/src/main/clojure/conexp/fca/distributivity.clj b/src/main/clojure/conexp/fca/distributivity.clj index 108c7c51a..e7180d81b 100644 --- a/src/main/clojure/conexp/fca/distributivity.clj +++ b/src/main/clojure/conexp/fca/distributivity.clj @@ -11,7 +11,8 @@ lattice." (:require [conexp.base :refer :all] [conexp.fca.contexts :refer :all] - [conexp.fca.implications :refer :all])) + [conexp.fca.implications :refer :all] + [clojure.set :refer [difference union subset? intersection]])) (defn birkhoff-downset-completion "Returns the downset birkhoff completion of a formal context. From 7163afbebe192a53c32b930854ed977b38741575 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Sat, 29 Jun 2024 16:11:42 +0200 Subject: [PATCH 108/117] Added Test Cycle --- .../clojure/conexp/fca/decompositions.clj | 61 ++++++++++++++++--- 1 file changed, 54 insertions(+), 7 deletions(-) diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index 7602bf95b..8b580478b 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -79,6 +79,43 @@ (make-lattice new-base-set #(subset? (first %1) (first %2)))) ) +(defn decomposable? [lat] + (let [top (lattice-one lat) + bot (lattice-zero lat) + decomp-pairs (into #{} (libkin-decomposition-pairs lat)) + non-trivial (disj (disj decomp-pairs [top bot]) [bot top])] + + (not (empty? non-trivial))) +) + + +(defn maximally-decomposable-filters [lat] + + (loop [queue [(lattice-zero lat)] + visited #{} + filters #{}] + + (if (empty? queue) + + filters + + (let [current-element (first queue) + current-filter (order-filter lat #{current-element}) + filter-lat (make-lattice-nc current-filter (inf lat) (sup lat))] + (if (decomposable? filter-lat) + (recur (subvec queue 1) ;remove first element + (set/union visited current-filter) + (conj filters filter-lat)) + (recur (into [] (distinct (concat (subvec queue 1) ;remove first element + (set/difference (lattice-upper-neighbours lat current-element) queue)))) + (conj visited current-element) + filters)))) +)) + + + + + (defn hierarchy [lat] "Computes the hierarchy lattice of all combinatorial decompositions." @@ -118,11 +155,10 @@ (make-lattice subctxs attr-intersection attr-union)) ) -(defn test-hierarchy [lat] +(defn test-hierarchy [hlat] "Verifies whether all meets and joins in the hierarchy lattice can be represented by attribute-union and attribute-intersection." - (let [hlat (hierarchy lat) - base (base-set hlat) + (let [base (base-set hlat) join (sup hlat) meet (inf hlat)] (for [lat1 base lat2 base] (if (and (= (join lat1 lat2) @@ -133,7 +169,7 @@ (context-from-lattice lat2))))) :OK (do (println "FALSE##################################") - (println (context-from-lattice lat)) + (println (context-from-lattice hlat)) (println (context-from-lattice lat1)) (println (context-from-lattice lat2)) ))) @@ -149,6 +185,15 @@ (println "FALSE#####################################"))) )) +(defn test-prime-factorization [hlat] + + (let [original (lattice-one hlat) + primes (lattice-atoms hlat)] + + (if (= (reduce combinatorial-product primes) original) :OK + (println "FALSE###########################")) +)) + (defn add-obj [ctx obj incidence] "Returns a new context with *obj* added." @@ -175,11 +220,13 @@ (defn test-cycle [number] (loop [counter number] - (let [ctx (reduce-attributes (random-context #{1 2 3 4 5} #{"A" "B" "C" "D" "E"} 0.5)) - lat (concept-lattice ctx)] + (let [ctx (reduce-attributes (random-context #{1 2 3 4 5 6} #{"A" "B" "C" "D" "E" "F"} 0.5)) + lat (concept-lattice ctx) + hlat (hierarchy lat)] - (doall (test-hierarchy lat)) + (doall (test-hierarchy hlat)) (doall (test-combi-decomp lat)) + (test-prime-factorization hlat) (if (not (= counter 0)) (recur (- counter 1)))))) From a360abce8b08d7fa6b9e45c80bc60104fe9c80a9 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Sun, 7 Jul 2024 15:37:28 +0200 Subject: [PATCH 109/117] Fixed Implementation of Decomposable filter Algorithm. --- .../clojure/conexp/fca/decompositions.clj | 28 ++++++++++++++----- 1 file changed, 21 insertions(+), 7 deletions(-) diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index 8b580478b..1bfbdc66e 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -96,27 +96,24 @@ filters #{}] (if (empty? queue) - filters (let [current-element (first queue) current-filter (order-filter lat #{current-element}) filter-lat (make-lattice-nc current-filter (inf lat) (sup lat))] (if (decomposable? filter-lat) - (recur (subvec queue 1) ;remove first element + (recur (into [] (remove #(.contains current-filter %) queue)) (set/union visited current-filter) (conj filters filter-lat)) (recur (into [] (distinct (concat (subvec queue 1) ;remove first element - (set/difference (lattice-upper-neighbours lat current-element) queue)))) + (set/difference (lattice-upper-neighbours lat current-element) + queue ;discard elements already in queue + visited)))) ;discard elements already visited (conj visited current-element) filters)))) )) - - - - (defn hierarchy [lat] "Computes the hierarchy lattice of all combinatorial decompositions." (let [pairs (libkin-decomposition-pairs lat) @@ -124,6 +121,12 @@ (make-lattice sublats #(subset? (base-set %1) (base-set %2)))) ) +(defn prime-factorization [lat] + (lattice-atoms (hierarchy lat)) + +) + + (defn attr-union [ctx1 ctx2] "Unifies the attributes of *ctx1* and *ctx2*. *ctx1* and *ctx2* must have the same objects." @@ -293,3 +296,14 @@ (def testctx (make-context #{1 2 3} #{"A" "B"} #{[1 "A"] [2 "B"]})) (def testctx2 (make-context #{1 2 3} #{"C"} #{})) + +(def bodiesofwater (make-context #{"puddle" "channel" "river" "canal" "lake" "reservoir" "sea"} + #{"temporary" "running" "inland" "natural" "stagant" "constant" "artificial" "maritime"} + + #{["puddle" "temporary"] ["puddle" "inland"] ["puddle" "natural"] ["puddle" "stagant"] + ["channel" "running"] ["channel" "inland"] ["channel" "constant"] + ["river" "running"] ["river" "inland"] ["river" "natural"] ["river" "constant"] + ["canal" "running"] ["canal" "inland"] ["canal" "constant"] ["canal" "artificial"] + ["lake" "inland"] ["lake" "natural"] ["lake" "stagant"] ["lake" "constant"] + ["reservoir" "inland"] ["reservoir" "stagant"] ["reservoir" "constant"] ["reservoir" "artificial"] + ["sea" "natural"] ["sea" "stagant"] ["sea" "constant"] ["sea" "maritime"]})) From 65388be9ba1def9fc2c8a490795a02164b1cedb0 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 18 Jul 2024 15:50:40 +0200 Subject: [PATCH 110/117] Restored Functionality --- .../clojure/conexp/fca/decompositions.clj | 17 ++++++-- src/main/clojure/conexp/fca/metrics.clj | 40 +++++++++++++++++++ 2 files changed, 53 insertions(+), 4 deletions(-) diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index 1bfbdc66e..5ae021c95 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -76,7 +76,7 @@ new-base-set (for [x con1 y con2] [(set/intersection (first x) (first y)) (set/union (second x) (second y))])] - (make-lattice new-base-set #(subset? (first %1) (first %2)))) + (make-lattice new-base-set #(set/subset? (first %1) (first %2)))) ) (defn decomposable? [lat] @@ -118,7 +118,7 @@ "Computes the hierarchy lattice of all combinatorial decompositions." (let [pairs (libkin-decomposition-pairs lat) sublats (set (flatten (for [p pairs] (combinatorial-decomposition-lattices lat p))))] - (make-lattice sublats #(subset? (base-set %1) (base-set %2)))) + (make-lattice sublats #(set/subset? (base-set %1) (base-set %2)))) ) (defn prime-factorization [lat] @@ -200,12 +200,12 @@ (defn add-obj [ctx obj incidence] "Returns a new context with *obj* added." - (make-context (union (objects ctx) #{obj}) (attributes ctx) incidence)) + (make-context (set/union (objects ctx) #{obj}) (attributes ctx) incidence)) (defn add-attr [ctx attr incidence] "Returns a new context with *attr* added." - (make-context (objects ctx) (union (attributes ctx) #{attr}) incidence)) + (make-context (objects ctx) (set/union (attributes ctx) #{attr}) incidence)) @@ -234,6 +234,7 @@ (recur (- counter 1)))))) + (def ctx-list #{"animals-d.ctx" "bird-diet-d.ctx" "bodiesofwater-d.ctx" @@ -307,3 +308,11 @@ ["lake" "inland"] ["lake" "natural"] ["lake" "stagant"] ["lake" "constant"] ["reservoir" "inland"] ["reservoir" "stagant"] ["reservoir" "constant"] ["reservoir" "artificial"] ["sea" "natural"] ["sea" "stagant"] ["sea" "constant"] ["sea" "maritime"]})) + + +(def ctx (read-context "testing-data/Bird-Diet.ctx")) +(def bc (birkhoff-upset-completion ctx)) +(def lat (concept-lattice ctx)) +(def bclat (concept-lattice bc)) +bclat +(decomposable? bclat) diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 166c0266e..4333de51a 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -11,6 +11,7 @@ [clojure.math.combinatorics :refer [permuted-combinations combinations]] ;; [clojure.math.numeric-tower :refer [log]] [conexp.base :refer :all] + [clojure.set :as set] [conexp.math.markov :refer :all] [conexp.fca [contexts :refer [make-context incidence dual-context @@ -27,6 +28,16 @@ bitwise-object-derivation bitwise-attribute-derivation concepts]] [implications :refer :all] + [lattices :refer [inf + sup + lattice-base-set + make-lattice + make-lattice-nc + concept-lattice + lattice-order + distributive? + lattice-one + lattice-zero]] [lattices :refer [inf sup lattice-base-set make-lattice concept-lattice lattice-order]]] [conexp.math.util :refer [eval-polynomial binomial-coefficient]] [clojure.set :refer [difference union subset? intersection]]) @@ -769,6 +780,35 @@ (let [atts (attributes ctx)] (take n (shuffle atts)))) +(defn neutral? [a lat] + (let [base-set (lattice-base-set lat) + join (sup lat) + meet (inf lat)] + (every? identity (for [x base-set y base-set] (= (meet (meet (join a x) (join a y)) (join x y)) + (join (join (meet a x) (meet a y)) (meet x y))))) +) +) + + + +;return all neutral elements in "lat" +(defn neutral-concepts [lat] + (let [base-set (lattice-base-set lat)] + (filter #(neutral? % lat) base-set) +) +) + + +;retruns all complements of "concept" in "lat" +(defn element-complement [concept lat] + (let [base-set (lattice-base-set lat)] + + (filter #(and (not= % concept) + (= ((sup lat) concept %) (lattice-one lat)) + (= ((inf lat) concept %) (lattice-zero lat))) + base-set)) +) + ;; (defn rel-consistency ??? ;; "Computes the relative consistency of a subset $N ⊆ M$ with respect to ;; a given formal context (G,M,I), and some attribute subset N ⊆ M" From 03b861a86296c38a53c41bb36b0913c5a953c713 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Mon, 22 Jul 2024 15:12:01 +0200 Subject: [PATCH 111/117] Added Algorithm for Maximal Intervals. --- .../clojure/conexp/fca/decompositions.clj | 91 +++++++++++++++++++ 1 file changed, 91 insertions(+) diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index 5ae021c95..20fbd4013 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -19,6 +19,12 @@ [clojure.set :as set])) +(defn interval [lat upper lower] + (let [order (lattice-order lat) + new-base-set (filter #(and (order % upper) (order lower %)) (base-set lat))] + (make-lattice-nc new-base-set order)) +) + (defn context-from-lattice [lat] "Computes the underlying context of a lattice by reading the incidence of all objects." "Does not work with the *lattice-product* method." @@ -113,6 +119,80 @@ filters)))) )) +(defn lattice-sort [a b lat] + (let [order (lattice-order lat)] + (if (= a b) 0 + (if (order a b) -1 + 1))) +) + + +(defn intervals-with-upper [lat upper] + + (loop [queue [(lattice-zero lat)] + visited #{} + intervals #{}] + + + (if (empty? queue) + intervals + + (let [current-element (first queue) + current-interval (interval lat upper current-element)] + + (if (not ((lattice-order lat) current-element upper)) + (recur (into [] (remove #(.contains (order-filter lat #{current-element}) %) queue)) + (set/union visited (order-filter lat #{current-element})) + intervals) + + (if (decomposable? current-interval) + (recur (into [] (remove #(.contains (order-filter lat #{current-element}) %) queue)) + (set/union visited (order-filter lat #{current-element})) + (conj intervals current-interval)) + (recur (into [] (distinct (concat (subvec queue 1) ;remove first element + (set/difference (lattice-upper-neighbours lat current-element) + queue ;discard elements already in queue + visited)))) ;discard elements already visited + (conj visited current-element) + intervals)))))) +) + + +(defn maximally-decomposable-intervals [lat] + (loop [queue (into [] (base-set lat)) + visited #{} + intervals #{}] + + (if (empty? queue) + + intervals + + (let [current-upper (first queue) + new-intervals (intervals-with-upper (make-lattice-nc (order-ideal lat #{current-upper}) (inf lat) (sup lat)) current-upper)] + + (if (empty? new-intervals) + + (recur (into [] (distinct (concat (subvec queue 1) ;remove first element + (set/difference (lattice-lower-neighbours lat current-upper) + queue ;discard elements already in queue + visited)))) ;discard elements already visited + (conj visited current-upper) + intervals) + + (recur (into [] (rest queue)) + (set/union visited (reduce #(set/union %1 (base-set %2)) #{} new-intervals)) + (set/union intervals new-intervals)))))) +) + + +(defn filter-maximal [intervals] + (into [] (filter #(not (some (fn [x] (and (set/subset? (base-set %) (base-set x)) + (not= % x))) intervals)) intervals)) + +) + + + (defn hierarchy [lat] "Computes the hierarchy lattice of all combinatorial decompositions." @@ -316,3 +396,14 @@ (def bclat (concept-lattice bc)) bclat (decomposable? bclat) + + + +(def ctx (read-context "testing-data/Animals.cxt")) + + +(def ctx (context-from-fcatools "animals_en.cxt")) +(def lat (concept-lattice ctx)) +(def max-int (filter-maximal (maximally-decomposable-intervals lat))) + +(sort #(< (count (base-set %1)) (count (base-set %2))) max-int) From 9789b7fea01c2b86559c0974b1039d1ec263d9d4 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Wed, 24 Jul 2024 12:50:19 +0200 Subject: [PATCH 112/117] Updated Algorithm for Decomposable Intervals. --- src/main/clojure/conexp/fca/decompositions.clj | 17 +++-------------- 1 file changed, 3 insertions(+), 14 deletions(-) diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index 20fbd4013..79e0a4cf5 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -160,7 +160,6 @@ (defn maximally-decomposable-intervals [lat] (loop [queue (into [] (base-set lat)) - visited #{} intervals #{}] (if (empty? queue) @@ -168,20 +167,10 @@ intervals (let [current-upper (first queue) - new-intervals (intervals-with-upper (make-lattice-nc (order-ideal lat #{current-upper}) (inf lat) (sup lat)) current-upper)] - - (if (empty? new-intervals) - - (recur (into [] (distinct (concat (subvec queue 1) ;remove first element - (set/difference (lattice-lower-neighbours lat current-upper) - queue ;discard elements already in queue - visited)))) ;discard elements already visited - (conj visited current-upper) - intervals) + new-intervals (maximally-decomposable-filters (make-lattice-nc (order-ideal lat #{current-upper}) (inf lat) (sup lat)))] - (recur (into [] (rest queue)) - (set/union visited (reduce #(set/union %1 (base-set %2)) #{} new-intervals)) - (set/union intervals new-intervals)))))) + (recur (into [] (rest queue)) + (set/union intervals new-intervals))))) ) From 58c0d68537c1119d836f53a147cbbe24fbb67837 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Thu, 21 Nov 2024 22:13:55 +0100 Subject: [PATCH 113/117] Started Cleanup. --- .../clojure/conexp/fca/decompositions.clj | 38 ++++++++----------- src/main/clojure/conexp/fca/lattices.clj | 6 +-- src/main/clojure/conexp/fca/metrics.clj | 2 +- 3 files changed, 20 insertions(+), 26 deletions(-) diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index 79e0a4cf5..a7d784b7e 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -20,31 +20,23 @@ (defn interval [lat upper lower] + "Returns a new Lattice Consisting of all Elements of *lat* that are Larger or Equal than *lower* + and are Lesser or Equal then *upper*." (let [order (lattice-order lat) new-base-set (filter #(and (order % upper) (order lower %)) (base-set lat))] (make-lattice-nc new-base-set order)) ) -(defn context-from-lattice [lat] - "Computes the underlying context of a lattice by reading the incidence of all objects." - "Does not work with the *lattice-product* method." - (let [concepts (base-set lat) - unions (reduce #(vector (set/union (first %1) (first %2)) (set/union (second %1) (second %2))) concepts) - objects (first unions) - attributes (second unions) - incidence (for [c concepts obj (first c) attr (second c)] [obj attr])] - (make-context objects attributes incidence) - )) - -(defn libkin-decomposition-pairs [lat] - "Returns all decompositions pair of *lat* for Libkin decompositions" + +(defn decomposition-pairs [lat] + "Returns all Decomposition Pairs / Neutral Complemented Elements in *lat*." (let [neutral-elements (neutral-concepts lat)] (for [n neutral-elements c (element-complement n lat)] [n c]))) (defn libkin-decomposition-lattices [lat decomp-pair] - "Computes the Lattices Resulting from the Libkin-Decomposition on the - Provided Decomposition Pair." + "Computes the Lattices Resulting from the Downset Decomposition on the + Provided Decomposition Pair." (let [set1 (order-ideal lat (conj #{} (first decomp-pair))) set2 (order-ideal lat (conj #{} (last decomp-pair))) order (lattice-order lat)] @@ -59,8 +51,8 @@ (sup lat))])) (defn combinatorial-decomposition-lattices [lat decomp-pair] - "Computes the Lattices Resulting from the Libkin-Decomposition on the - Provided Decomposition Pair." + "Computes the Lattices Resulting from the Upset Decomposition on the + Provided Decomposition Pair." (let [set1 (order-filter lat (conj #{} (first decomp-pair))) set2 (order-filter lat (conj #{} (last decomp-pair))) order (lattice-order lat)] @@ -74,9 +66,10 @@ (inf lat) (sup lat))])) -(defn combinatorial-product [a b] - "Computes the combinatoial produce of two lattices. - May fail if *a* and *b* are not complemented neutral ideals of the same lattice" +;Downset Product TODO + +(defn upset-product [a b] + "Computes the Upset Product of two Lattices that are Complemented Neutral Ideals is Another Lattice." (let [con1 (base-set a) con2 (base-set b) new-base-set (for [x con1 y con2] @@ -86,17 +79,18 @@ ) (defn decomposable? [lat] + "Verifies Whether the Supplied Lattice has non-trivial Decomposition Pairs." (let [top (lattice-one lat) bot (lattice-zero lat) decomp-pairs (into #{} (libkin-decomposition-pairs lat)) - non-trivial (disj (disj decomp-pairs [top bot]) [bot top])] + non-trivial (disj (disj decomp-pairs [top bot]) [bot top])] (not (empty? non-trivial))) ) (defn maximally-decomposable-filters [lat] - + "Returns all Maximally Decomposable Principal Filters of the Supplied Lattice." (loop [queue [(lattice-zero lat)] visited #{} filters #{}] diff --git a/src/main/clojure/conexp/fca/lattices.clj b/src/main/clojure/conexp/fca/lattices.clj index ee6bad48c..973c0bb07 100644 --- a/src/main/clojure/conexp/fca/lattices.clj +++ b/src/main/clojure/conexp/fca/lattices.clj @@ -12,10 +12,10 @@ conexp.math.algebra conexp.fca.contexts conexp.fca.posets - [clojure.math.combinatorics :refer [cartesian-product]])) - conexp.fca.posets) + [clojure.math.combinatorics :refer [cartesian-product]]) (:require [clojure.set :refer [difference union subset? intersection]]) - (:gen-class)) +) + ;;; Datastructure diff --git a/src/main/clojure/conexp/fca/metrics.clj b/src/main/clojure/conexp/fca/metrics.clj index 1b9858f87..9442d21cd 100644 --- a/src/main/clojure/conexp/fca/metrics.clj +++ b/src/main/clojure/conexp/fca/metrics.clj @@ -9,7 +9,7 @@ (ns conexp.fca.metrics (:require [clojure.core.reducers :as r] [clojure.math.combinatorics :refer [permuted-combinations combinations]] - [clojure.set :as set] + [clojure.set :refer [difference union subset? intersection]] ;; [clojure.math.numeric-tower :refer [log]] [conexp.base :refer :all] [conexp.math.markov :refer :all] From 8a47087c532cbf50913737d5163c53d7f1890924 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Sat, 23 Nov 2024 22:57:03 +0100 Subject: [PATCH 114/117] Updated Test. --- animals-d.ctx | 15 - bird-diet-d.ctx | 29 -- bodiesofwater-d.ctx | 30 -- booth-d.ctx | 128 ------- brunson-club-d.ctx | 36 -- cointoss-2-d.ctx | 137 -------- diagnosis-d.ctx | 132 ------- digits-d.ctx | 28 -- dirichlet-1-d.ctx | 326 ------------------ dolphins-d.ctx | 87 ----- drive_concepts_for_motorcars-d.ctx | 33 -- forum-romanum-d.ctx | 27 -- gewuerzplaner-d.ctx | 62 ---- living-beings-and-water-d.ctx | 22 -- myctx-d.ctx | 17 - olympic-disciplines-d.ctx | 66 ---- seasoning-planner-d.ctx | 62 ---- southern-woman-d.ctx | 39 --- .../clojure/conexp/fca/decompositions.clj | 282 ++++----------- .../conexp/fca/decompositions_test.clj | 67 ++-- testcontext-d.ctx | 14 - triangles-d.ctx | 21 -- wood-properties-d.ctx | 45 --- zoo-d.ctx | 134 ------- 24 files changed, 105 insertions(+), 1734 deletions(-) delete mode 100644 animals-d.ctx delete mode 100644 bird-diet-d.ctx delete mode 100644 bodiesofwater-d.ctx delete mode 100644 booth-d.ctx delete mode 100644 brunson-club-d.ctx delete mode 100644 cointoss-2-d.ctx delete mode 100644 diagnosis-d.ctx delete mode 100644 digits-d.ctx delete mode 100644 dirichlet-1-d.ctx delete mode 100644 dolphins-d.ctx delete mode 100644 drive_concepts_for_motorcars-d.ctx delete mode 100644 forum-romanum-d.ctx delete mode 100644 gewuerzplaner-d.ctx delete mode 100644 living-beings-and-water-d.ctx delete mode 100644 myctx-d.ctx delete mode 100644 olympic-disciplines-d.ctx delete mode 100644 seasoning-planner-d.ctx delete mode 100644 southern-woman-d.ctx delete mode 100644 testcontext-d.ctx delete mode 100644 triangles-d.ctx delete mode 100644 wood-properties-d.ctx delete mode 100644 zoo-d.ctx diff --git a/animals-d.ctx b/animals-d.ctx deleted file mode 100644 index 57ecc270a..000000000 --- a/animals-d.ctx +++ /dev/null @@ -1,15 +0,0 @@ -B - -3 -4 - -bird -penguin -pidgeon -eggs -cannot fly -warm-blooded -can fly -X.X. -XXX. -X.XX diff --git a/bird-diet-d.ctx b/bird-diet-d.ctx deleted file mode 100644 index cb621e0d6..000000000 --- a/bird-diet-d.ctx +++ /dev/null @@ -1,29 +0,0 @@ -B - -10 -4 - -fink -baumläufer -zaunkönig -kleiber -dompfaff -amsel -wintergoldhähnchen -girlitz -sperling -meise -sonnenblume -beeren -haferflocken -äpfel -X... -..X. -.... -X... -XX.. -.XXX -.... -.... -X.X. -X... diff --git a/bodiesofwater-d.ctx b/bodiesofwater-d.ctx deleted file mode 100644 index e416acad8..000000000 --- a/bodiesofwater-d.ctx +++ /dev/null @@ -1,30 +0,0 @@ -B - -10 -5 - -river -stream -reservoir -puddle -sea -lagoon -rivulet -runnel -trickle -torrent -running -maritime -constant -natural -stagnant -X.XX. -X.XX. -..X.X -...XX -.XXXX -.XXXX -X.XX. -X.XX. -X.XX. -X.XX. diff --git a/booth-d.ctx b/booth-d.ctx deleted file mode 100644 index 5e078b5a0..000000000 --- a/booth-d.ctx +++ /dev/null @@ -1,128 +0,0 @@ -B - -48 -27 - -Obj 41 -Obj 32 -Obj 47 -Obj 28 -Obj 1 -Obj 63 -Obj 40 -Obj 60 -Obj 5 -Obj 46 -Obj 53 -Obj 57 -Obj 2 -Obj 62 -Obj 39 -Obj 61 -Obj 36 -Obj 44 -Obj 59 -Obj 17 -Obj 38 -Obj 11 -Obj 45 -Obj 8 -Obj 50 -Obj 4 -Obj 25 -Obj 14 -Obj 15 -Obj 27 -Obj 65 -Obj 64 -Obj 3 -Obj 51 -Obj 37 -Obj 29 -Obj 19 -Obj 48 -Obj 10 -Obj 30 -Obj 43 -Obj 49 -Obj 52 -Obj 13 -Obj 9 -Obj 42 -Obj 16 -Obj 7 -NADHO1 -NADHI0 -ROSI0 -BileI1 -ROSO0 -BileO2 -ROSO2 -NecrO2 -ROSO1 -BileO1 -CaI0 -AntiOxI2 -AntiOxO1 -NADHO2 -CaO1 -ApI1 -NADHI1 -NecrI2 -CaO2 -ApI0 -NecrI0 -BileI2 -AntiOxI1 -NecrI1 -ApI2 -AntiOxO2 -ROSI1 -...X..X.XXX...X.X..XX.....X -...X.XX.XX..X.X.X..XXXX...X -X..X..X.XXX...X.X..XX.....X -...X.XXXXXX.X.X.X..XXXX...X -X.......X.X.X...X..XX.X...X -...X.XX.XX....X.X..XXX....X -...X..X.XXX...X.X..XX.....X -...X.XX.XXX...X.X..XXX....X -...X..X.XXX.X.X.X..XX.X...X -...X..X.XX....X.X..XX.....X -...X..X.XX....X.X..XX.....X -X..X.XX.XXX..XX.X.XXXX....X -X..X..X.XXX.X.X.X..XX.X...X -...X.XX.XX....X.X..XXX....X -...X..X.XXX.....X..XX.....X -X..X.XX.XX....X.X..XXX....X -X..X..X.XXX...X.X..XX.....X -...X..X.XX......X..XX.....X -...X.XX.XXX...X.X..XXX....X -...X..X.XXX.X.X.X..XX.X...X -X..X..X.XXX...X.X..XX.....X -...X..X.XX..X.X.X..XX.X...X -...X..X.XX....X.X..XX.....X -X..X..X.XX..X...X..XX.X...X -...X..X.XXX...X.X..XX.....X -...X..X.XXX.X...X..XX.X...X -X..X.XX.XXX.XXX.X.XXXXX...X -X..X..X.XXX.X.X.X..XX.X...X -X..X..X.XXX.X...X..XX.X...X -...X.XX.XXX.X.X.X..XXXX...X -...X.XX.XX....X.X..XXX....X -...X.XX.XX....X.X..XXX....X -X..X..X.XXX.X...X..XX.X...X -...X..X.XX......X..XX.....X -X..X..X.XXX.....X..XX.....X -X..X.XX.XX..X.X.X..XXXX...X -...X..X.XXX.X...X..XX.X...X -...X..X.XXX.....X..XX.....X -X..X..X.XX..X.X.X..XX.X...X -...X.XX.XX..X.X.X..XXXX...X -X..X..X.XX....X.X..XX.....X -...X..X.XXX...X.X..XX.....X -...X..X.XX....X.X..XX.....X -...X..X.XX..X...X..XX.X...X -...X..X.XX..X...X..XX.X...X -X..X..X.XX......X..XX.....X -...X..X.XXX.X...X..XX.X...X -...X..X.XXX.X...X..XX.X...X diff --git a/brunson-club-d.ctx b/brunson-club-d.ctx deleted file mode 100644 index 5e0c1d348..000000000 --- a/brunson-club-d.ctx +++ /dev/null @@ -1,36 +0,0 @@ -B - -11 -9 - -U_17 -U_3 -U_4 -U_10 -U_24 -U_14 -U_11 -U_22 -U_9 -U_18 -U_5 -C_12 -C_11 -C_9 -C_13 -C_14 -C_2 -C_3 -C_10 -C_4 -..X.X...X -......... -......... -....X.... -......... -......... -..X...X.. -......... -....X.... -X.X.X.X.. -......... diff --git a/cointoss-2-d.ctx b/cointoss-2-d.ctx deleted file mode 100644 index 795b6e8ee..000000000 --- a/cointoss-2-d.ctx +++ /dev/null @@ -1,137 +0,0 @@ -B - -62 -8 - -191 -58 -180 -88 -108 -9 -93 -83 -188 -50 -141 -157 -87 -195 -118 -196 -14 -116 -59 -89 -61 -169 -179 -192 -167 -98 -73 -78 -186 -44 -100 -173 -53 -36 -12 -140 -166 -75 -194 -76 -6 -120 -70 -0 -95 -153 -74 -37 -46 -124 -56 -85 -126 -2 -54 -103 -31 -164 -163 -92 -79 -117 -9 -3 -4 -8 -7 -13 -1 -2 -........ -........ -...X...X -........ -.X..X.XX -......X. -........ -........ -........ -........ -...X...X -.......X -.......X -...X.... -...X..X. -...X.... -......X. -........ -.......X -.XXX..X. -......X. -......X. -........ -........ -........ -.......X -........ -........ -........ -........ -.......X -........ -........ -...X.... -........ -........ -...X..XX -...X.... -........ -........ -......X. -...X.... -......XX -...X.... -........ -........ -...X...X -......XX -...X.... -......X. -.......X -........ -........ -.......X -........ -........ -........ -........ -...X...X -........ -.......X -...X.... diff --git a/diagnosis-d.ctx b/diagnosis-d.ctx deleted file mode 100644 index 41a6bcf06..000000000 --- a/diagnosis-d.ctx +++ /dev/null @@ -1,132 +0,0 @@ -B - -59 -9 - -Patient#111 -Patient#119 -Patient#31 -Patient#96 -Patient#77 -Patient#17 -Patient#105 -Patient#74 -Patient#90 -Patient#65 -Patient#69 -Patient#18 -Patient#63 -Patient#97 -Patient#60 -Patient#9 -Patient#83 -Patient#61 -Patient#118 -Patient#21 -Patient#115 -Patient#20 -Patient#71 -Patient#29 -Patient#25 -Patient#16 -Patient#70 -Patient#1 -Patient#68 -Patient#109 -Patient#62 -Patient#104 -Patient#8 -Patient#86 -Patient#116 -Patient#110 -Patient#92 -Patient#64 -Patient#23 -Patient#100 -Patient#3 -Patient#80 -Patient#82 -Patient#67 -Patient#24 -Patient#94 -Patient#66 -Patient#26 -Patient#102 -Patient#89 -Patient#10 -Patient#107 -Patient#113 -Patient#79 -Patient#101 -Patient#6 -Patient#13 -Patient#73 -Patient#35 -[Lumbar pain yes] -[Bladder inflammation? yes] -[Nausea no] -[Burning yes] -[Temperatur [∈ [35.0 37.5]]] -[Micturition pains yes] -[Nausea yes] -[Pelvis nephritis? yes] -[Urine pushing yes] -..X...... -X.XX...XX -.XX.XX..X -X.XX...XX -X.XX...XX -.XXXXX..X -XX.X.XXXX -..X...... -..X...... -X.XX...XX -X.XX...XX -.XXXXX..X -X.XX...XX -X.XX...XX -X.XX...XX -.XXXXX..X -XX.X.XXXX -X.XX...XX -X.XX...XX -.XX.XX..X -X.XX...XX -.XX.XX..X -XX.X.XXXX -.XXXXX..X -.XXXXX..X -.XXXXX..X -XX.X.XXXX -.XXXXX..X -X.XX...XX -X.XX...XX -X.XX...XX -X.XX...XX -.XXXXX..X -..X...... -..X...... -XX.X.XXXX -XX.X.XXXX -X.XX...XX -.XXXXX..X -X.XX...XX -.XXXXX..X -..X...... -X.XX...XX -X.XX...XX -.XXXXX..X -..X...... -X.XX...XX -.XXXXX..X -..X...... -XX.X.XXXX -.XXXXX..X -..X...... -X.XX...XX -XX.X.XXXX -XX.X.XXXX -.XXXXX..X -.XXXXX..X -..X...... -.XXXXX..X diff --git a/digits-d.ctx b/digits-d.ctx deleted file mode 100644 index 088b7e5c0..000000000 --- a/digits-d.ctx +++ /dev/null @@ -1,28 +0,0 @@ -B - -8 -7 - -9 -3 -4 -8 -7 -5 -1 -0 -d -f -e -a -b -g -c -XX.XXX. -.X.XXXX -XX..XX. -XXXXXXX -.X.X.X. -X..XXXX -.X...X. -XXXX.XX diff --git a/dirichlet-1-d.ctx b/dirichlet-1-d.ctx deleted file mode 100644 index 821ad5679..000000000 --- a/dirichlet-1-d.ctx +++ /dev/null @@ -1,326 +0,0 @@ -B - -158 -5 - -191 -58 -180 -88 -108 -93 -158 -51 -50 -141 -139 -157 -185 -49 -175 -155 -87 -26 -4 -8 -118 -193 -105 -28 -60 -196 -14 -135 -123 -101 -89 -61 -57 -179 -68 -30 -21 -156 -96 -159 -80 -162 -192 -33 -20 -67 -113 -81 -167 -98 -19 -17 -25 -115 -78 -111 -172 -176 -119 -15 -42 -7 -128 -186 -66 -152 -181 -44 -5 -184 -100 -48 -106 -173 -53 -90 -190 -112 -18 -36 -148 -12 -137 -140 -27 -166 -121 -62 -75 -194 -168 -24 -35 -154 -6 -110 -174 -171 -99 -38 -149 -70 -144 -134 -39 -1 -146 -63 -84 -177 -0 -43 -125 -104 -95 -153 -74 -142 -46 -127 -11 -109 -138 -45 -114 -56 -32 -133 -147 -55 -182 -85 -189 -126 -2 -143 -178 -72 -170 -103 -91 -10 -65 -161 -129 -187 -31 -71 -164 -163 -64 -92 -23 -79 -160 -29 -150 -132 -att_0 -att_8 -att_6 -att_1 -att_2 -..... -.X.XX -X..X. -XX..X -...X. -..... -.X... -XX... -X..XX -.X.XX -...X. -..X.X -XX... -X..XX -..... -..... -X.... -.X.X. -..... -.X..X -XX.X. -XX... -XX.XX -..... -.X... -...XX -.X.X. -.X..X -X.... -X.XXX -....X -....X -.X.X. -XX... -.X.X. -.X.X. -X.... -XX... -X.... -X.... -X.... -X..X. -XX.X. -.X... -..X.X -.XX.X -.X..X -....X -.X..X -..X.X -.X.XX -X.X.X -..X.X -.X.XX -XXX.X -X.... -X.... -XXX.X -.X..X -X.... -XX..X -XXX.X -XX..X -XX... -.X.X. -..... -..... -..XXX -X.... -X..XX -XXXXX -XX.X. -.X.X. -XX... -..... -X..X. -X..X. -.X... -....X -....X -.XXXX -X...X -..X.X -....X -XX... -..... -X...X -..... -XX... -XX... -XX.X. -.X..X -...X. -..XXX -.X... -.X... -..XXX -X.X.X -X.... -.X... -XX... -....X -X...X -X..X. -XX... -...XX -..X.X -.X.XX -X..X. -....X -X.... -..... -....X -.X.XX -..X.X -....X -X...X -...XX -.XX.X -X..X. -.X..X -X.... -....X -X...X -X..X. -...X. -....X -.X..X -...X. -X.... -X.... -XX... -.X.XX -X...X -XX..X -.X... -.XX.X -.X.X. -XX... -..... -.X... -X.X.X -..XXX -XX.X. -.X.X. -X..X. -X...X -...XX -....X -.XX.X -....X -.X.XX -..X.X -...X. -XX... -XXX.X -X.... -XX... diff --git a/dolphins-d.ctx b/dolphins-d.ctx deleted file mode 100644 index d9aa30dbd..000000000 --- a/dolphins-d.ctx +++ /dev/null @@ -1,87 +0,0 @@ -B - -28 -26 - -U_58 -U_17 -U_3 -U_35 -U_28 -U_61 -U_42 -U_4 -U_62 -U_40 -U_32 -U_10 -U_24 -U_14 -U_60 -U_29 -U_57 -U_49 -U_9 -U_45 -U_21 -U_56 -U_23 -U_13 -U_12 -U_33 -U_59 -U_5 -A_37 -A_1 -A_13 -A_30 -A_12 -A_17 -A_53 -A_48 -A_41 -A_9 -A_24 -A_31 -A_47 -A_32 -A_19 -A_25 -A_56 -A_28 -A_44 -A_59 -A_20 -A_5 -A_36 -A_57 -A_22 -A_23 -.......................... -.......................... -.......................... -.......................... -.......................... -.......................... -.......................... -.........X................ -.......................... -X......................... -.......................... -.......................... -X......................... -.......................... -X........X................ -.......X.X.X.............. -.......................... -.......................... -.......................... -.......................... -X....X.X.X....X........... -.......................... -.......................... -.......................... -.......................... -.......................... -.......................... -.......................... diff --git a/drive_concepts_for_motorcars-d.ctx b/drive_concepts_for_motorcars-d.ctx deleted file mode 100644 index 4ec145f36..000000000 --- a/drive_concepts_for_motorcars-d.ctx +++ /dev/null @@ -1,33 +0,0 @@ -B - -5 -18 - -Conventional -All-wheel -Rear-wheel -Mid-engine -Front-wheel -E+ -C-l -E- -C-h -De+ -Dl+ -C-vl -E++ -S-u/n -Dl++ -Dl- -R+ -S-n -De++ -M-- -M- -R++ -E-- -X....X.....X...... -X..XXX..XX.X.X.X.. -.XX.XX...X...X.... -.XX.XX...X.XXXXX.X -XX..X.XX..XX....X. diff --git a/forum-romanum-d.ctx b/forum-romanum-d.ctx deleted file mode 100644 index a33bd7871..000000000 --- a/forum-romanum-d.ctx +++ /dev/null @@ -1,27 +0,0 @@ -B - -8 -6 - -Basilica of Maxentius -Temple of Vesta -Arch of Septimus Severus -Temple of Antonius and Fausta -Curia -Phocas column -Temple of Castor and Pollux -Arch of Titus -GB2 -M2 -GB1 -B -M1 -M3 -...X.. -XXX.X. -.XXXX. -.XXXXX -...... -.XX.X. -XXXXXX -XXXXX. diff --git a/gewuerzplaner-d.ctx b/gewuerzplaner-d.ctx deleted file mode 100644 index 3d9379683..000000000 --- a/gewuerzplaner-d.ctx +++ /dev/null @@ -1,62 +0,0 @@ -B - -20 -17 - -Gedünsteter Fisch -Kräuterquark/Dips -Rindfleisch -Bratkartoffeln -Gebratener Fisch -Gulasch -Risotto/Paella -Kartoffelauflauf/-gratin -Bowle -Desserts -Püree -Käsegebäck -Gegrillter Fisch -Kuchen -Gebackener Fisch -Rouladen -Blechkartoffeln -Punch/Tee -Obstsalat -Kalbfleisch -Estragon gerebelt -Verschiedenes(Gruppierung) -Fisch(Gruppierung) -Paprika “Rosen” gemahlen -Gemüse(Gruppierung) -Oregano gerebelt -Saucen(Gruppierung) -Piment gemahlen -Curry gemahlen -Wacholderbeeren -Geflügel(Gruppierung) -Bohnenkraut gerebelt -Knoblauch granuliert -Kurkuma -Beifuß gemahlen -Koriander gemahlen -Majoran gerebelt -..X.....X...X.... -XX.X.X..X...XX.X. -........X...X.... -...X........X.... -..XX.X..X...X.... -...X........X.... -........X...X.... -................. -................. -................. -................. -................. -..X.....X...X.... -................. -..X.....X...X.... -................. -...X........X.... -................. -................. -........X...X.... diff --git a/living-beings-and-water-d.ctx b/living-beings-and-water-d.ctx deleted file mode 100644 index c6ba10bab..000000000 --- a/living-beings-and-water-d.ctx +++ /dev/null @@ -1,22 +0,0 @@ -B - -6 -5 - -dog -fish leech -corn -water weeds -bean -reed -has limbs -breast feeds -needs chlorophyll -needs water to live -lives on land -XX.XX -...X. -..XXX -..XX. -..XXX -..XXX diff --git a/myctx-d.ctx b/myctx-d.ctx deleted file mode 100644 index b4f4afb55..000000000 --- a/myctx-d.ctx +++ /dev/null @@ -1,17 +0,0 @@ -B - -4 -4 - -3 -1 -353 -2 -3 -2344 -23423 -1 -X... -...X -.... -.... diff --git a/olympic-disciplines-d.ctx b/olympic-disciplines-d.ctx deleted file mode 100644 index 46854bae7..000000000 --- a/olympic-disciplines-d.ctx +++ /dev/null @@ -1,66 +0,0 @@ -B - -24 -13 - -Judo – Judo -Aquatics – Swimming -Sport Climbing – Sport Climbing -Cycling – Track -Golf – Golf -Handball – Handball -Rugby – Rugby Sevens -Volleyball – Volleyball -Baseball/Softball – Baseball/Softball -Cycling – Mountain Bike -Karate – Kumite -Cycling – BMX Racing -Fencing – Fencing -Gymnastics – Rhythmic -Volleyball – Beach Volleyball -Basketball – Basketball -Tennis – Tennis -Karate – Kata -Archery – Archery -Weightlifting – Weightlifting -Skateboarding – Skateboarding -Basketball – 3x3 -Gymnastics – Trampoline -Cycling – BMX Freestyle -female only events -indoor events -mixed events -male only events -has paralympic equivalent -individual competition -open events -part of >= 16 olympics ->= 10 events -water sport -part of >= 24 olympics -combat sport ->= 20 events -XXXXXX..X..X. -XXXXXX.XXXX.X -XX.X.X....... -XX.XXX.XX.X.. -X..X.X....... -XX.X......... -X..XX........ -XX.XX........ -X..X......... -X..X.X....... -XX.X.X.....X. -X..X.X....... -XX.XXX.XX.XX. -XX...X....... -X..X......... -XX.XX..X..... -X.XXXX.X..... -XX.X.X.....X. -X.XXXX.X...X. -XX.XXX.XX.X.. -X..X.X....... -XX.X......... -XX.X.X....... -X..X.X....... diff --git a/seasoning-planner-d.ctx b/seasoning-planner-d.ctx deleted file mode 100644 index 3d9379683..000000000 --- a/seasoning-planner-d.ctx +++ /dev/null @@ -1,62 +0,0 @@ -B - -20 -17 - -Gedünsteter Fisch -Kräuterquark/Dips -Rindfleisch -Bratkartoffeln -Gebratener Fisch -Gulasch -Risotto/Paella -Kartoffelauflauf/-gratin -Bowle -Desserts -Püree -Käsegebäck -Gegrillter Fisch -Kuchen -Gebackener Fisch -Rouladen -Blechkartoffeln -Punch/Tee -Obstsalat -Kalbfleisch -Estragon gerebelt -Verschiedenes(Gruppierung) -Fisch(Gruppierung) -Paprika “Rosen” gemahlen -Gemüse(Gruppierung) -Oregano gerebelt -Saucen(Gruppierung) -Piment gemahlen -Curry gemahlen -Wacholderbeeren -Geflügel(Gruppierung) -Bohnenkraut gerebelt -Knoblauch granuliert -Kurkuma -Beifuß gemahlen -Koriander gemahlen -Majoran gerebelt -..X.....X...X.... -XX.X.X..X...XX.X. -........X...X.... -...X........X.... -..XX.X..X...X.... -...X........X.... -........X...X.... -................. -................. -................. -................. -................. -..X.....X...X.... -................. -..X.....X...X.... -................. -...X........X.... -................. -................. -........X...X.... diff --git a/southern-woman-d.ctx b/southern-woman-d.ctx deleted file mode 100644 index 4ac3435d3..000000000 --- a/southern-woman-d.ctx +++ /dev/null @@ -1,39 +0,0 @@ -B - -12 -10 - -Frances Anderson -Flora Price -Sylvia Avondale -Ruth DeSand -Theresa Anderson -Helen Lloyd -Eleanor Nye -Olivia Carleton -Dorothy Murchison -Nora Fayette -Katherina Rogers -Pearl Oglethorpe -E7 -E12 -E1 -E9 -E8 -E2 -E10 -E13 -E4 -E14 -....X..... -...X...... -XX.XX.XX.X -X..XX..... -X..XXX..X. -XX..X.X... -X...X..... -...X...... -...XX..... -XX.X..XX.X -.X.XX.XX.X -...XX..... diff --git a/src/main/clojure/conexp/fca/decompositions.clj b/src/main/clojure/conexp/fca/decompositions.clj index a7d784b7e..b97ec703e 100644 --- a/src/main/clojure/conexp/fca/decompositions.clj +++ b/src/main/clojure/conexp/fca/decompositions.clj @@ -18,6 +18,16 @@ [posets :refer :all]] [clojure.set :as set])) +(defn context-from-lattice [lat] + "Computes the underlying context of a lattice by reading the incidence of all objects." + "Does not work with the *lattice-product* method." + (let [concepts (base-set lat) + unions (reduce #(vector (set/union (first %1) (first %2)) (set/union (second %1) (second %2))) concepts) + objects (first unions) + attributes (second unions) + incidence (for [c concepts obj (first c) attr (second c)] [obj attr])] + (make-context objects attributes incidence)) +) (defn interval [lat upper lower] "Returns a new Lattice Consisting of all Elements of *lat* that are Larger or Equal than *lower* @@ -34,7 +44,7 @@ (for [n neutral-elements c (element-complement n lat)] [n c]))) -(defn libkin-decomposition-lattices [lat decomp-pair] +(defn downset-decomposition-lattices [lat decomp-pair] "Computes the Lattices Resulting from the Downset Decomposition on the Provided Decomposition Pair." (let [set1 (order-ideal lat (conj #{} (first decomp-pair))) @@ -50,7 +60,7 @@ (inf lat) (sup lat))])) -(defn combinatorial-decomposition-lattices [lat decomp-pair] +(defn upset-decomposition-lattices [lat decomp-pair] "Computes the Lattices Resulting from the Upset Decomposition on the Provided Decomposition Pair." (let [set1 (order-filter lat (conj #{} (first decomp-pair))) @@ -66,7 +76,15 @@ (inf lat) (sup lat))])) -;Downset Product TODO +(defn downset-product [a b] + "Computes the Downset Product of two Lattices that are Complemented Neutral Ideals is Another Lattice." + (let [con1 (base-set a) + con2 (base-set b) + new-base-set (for [x con1 y con2] + [(set/union (first x) (first y)) + (set/intersection (second x) (second y))])] + (make-lattice new-base-set #(set/subset? (first %1) (first %2)))) +) (defn upset-product [a b] "Computes the Upset Product of two Lattices that are Complemented Neutral Ideals is Another Lattice." @@ -82,7 +100,7 @@ "Verifies Whether the Supplied Lattice has non-trivial Decomposition Pairs." (let [top (lattice-one lat) bot (lattice-zero lat) - decomp-pairs (into #{} (libkin-decomposition-pairs lat)) + decomp-pairs (into #{} (decomposition-pairs lat)) non-trivial (disj (disj decomp-pairs [top bot]) [bot top])] (not (empty? non-trivial))) @@ -113,52 +131,21 @@ filters)))) )) -(defn lattice-sort [a b lat] - (let [order (lattice-order lat)] - (if (= a b) 0 - (if (order a b) -1 - 1))) -) - - -(defn intervals-with-upper [lat upper] - - (loop [queue [(lattice-zero lat)] - visited #{} - intervals #{}] - - - (if (empty? queue) - intervals - (let [current-element (first queue) - current-interval (interval lat upper current-element)] - - (if (not ((lattice-order lat) current-element upper)) - (recur (into [] (remove #(.contains (order-filter lat #{current-element}) %) queue)) - (set/union visited (order-filter lat #{current-element})) - intervals) - - (if (decomposable? current-interval) - (recur (into [] (remove #(.contains (order-filter lat #{current-element}) %) queue)) - (set/union visited (order-filter lat #{current-element})) - (conj intervals current-interval)) - (recur (into [] (distinct (concat (subvec queue 1) ;remove first element - (set/difference (lattice-upper-neighbours lat current-element) - queue ;discard elements already in queue - visited)))) ;discard elements already visited - (conj visited current-element) - intervals)))))) +(defn- discard-non-maximal [intervals] + "Receives a Set of Concept Lattices and Discards all that are not Maximal in Respect to Set Inclusion of the Base Set." + (into [] (filter #(not (some (fn [x] (and (set/subset? (base-set %) (base-set x)) + (not= % x))) intervals)) intervals)) ) - (defn maximally-decomposable-intervals [lat] + "Returns all Maximally Decomposable Intervals of the Supplied Lattice." (loop [queue (into [] (base-set lat)) intervals #{}] (if (empty? queue) - intervals + (discard-non-maximal intervals) (let [current-upper (first queue) new-intervals (maximally-decomposable-filters (make-lattice-nc (order-ideal lat #{current-upper}) (inf lat) (sup lat)))] @@ -168,24 +155,40 @@ ) -(defn filter-maximal [intervals] - (into [] (filter #(not (some (fn [x] (and (set/subset? (base-set %) (base-set x)) - (not= % x))) intervals)) intervals)) + +(defn direct-decomposition-lattice [lat] + "Computes the (Upset) Direct Decomposition Lattice of the Supplied Concept Lattice." + (let [pairs (decomposition-pairs lat) + sublats (set (flatten (for [p pairs] (upset-decomposition-lattices lat p))))] + (make-lattice sublats #(set/subset? (base-set %1) (base-set %2)))) ) +(defn prime-factorization [lat] + "Returs a Prime Factorization of the Supplied Lattice." + (lattice-atoms (direct-decomposition-lattice lat)) +) +(defn obj-union [ctx1 ctx2] + "Unifies the objects of *ctx1* and *ctx2*. + *ctx1* and *ctx2* must have the same attributes." + (if (not (= (attributes ctx1) (attributes ctx2))) + (println "Contexts do not have the same attributes!") + (make-context (set/union (objects ctx1) (objects ctx2)) + (attributes ctx1) + (set/union (incidence ctx1) (incidence ctx2)))) -(defn hierarchy [lat] - "Computes the hierarchy lattice of all combinatorial decompositions." - (let [pairs (libkin-decomposition-pairs lat) - sublats (set (flatten (for [p pairs] (combinatorial-decomposition-lattices lat p))))] - (make-lattice sublats #(set/subset? (base-set %1) (base-set %2)))) ) -(defn prime-factorization [lat] - (lattice-atoms (hierarchy lat)) +(defn obj-intersection [ctx1 ctx2] + "Intersects the objects of *ctx1* and *ctx2*. + *ctx1* and *ctx2* must have the same attributes." + (if (not (= (attributes ctx1) (attributes ctx2))) + (println "Contexts do not have the same attributes!") + (make-context (set/intersection (objects ctx1) (objects ctx2)) + (attributes ctx1) + (set/intersection (incidence ctx1) (incidence ctx2)))) ) @@ -212,181 +215,12 @@ ) -(defn ctx-hierarchy [lat] - "Computes the hierarchy lattice of the contexts of all combinatoiral decompositions." - (let [pairs (libkin-decomposition-pairs lat) - sublats (set (flatten (for [p pairs] (combinatorial-decomposition-lattices lat p)))) +(defn ctx-decomposition-lattice [lat] + "Computes the (Upset) Direct Decomposition Lattice in Terms of each Elements Underlying Formal Context." + (let [pairs (decomposition-pairs lat) + sublats (set (flatten (for [p pairs] (upset-decomposition-lattices lat p)))) subctxs (map context-from-lattice sublats)] (make-lattice subctxs attr-intersection attr-union)) ) -(defn test-hierarchy [hlat] - "Verifies whether all meets and joins in the hierarchy lattice can be represented by attribute-union - and attribute-intersection." - (let [base (base-set hlat) - join (sup hlat) - meet (inf hlat)] - (for [lat1 base lat2 base] (if (and (= (join lat1 lat2) - (concept-lattice (attr-union (context-from-lattice lat1) - (context-from-lattice lat2)))) - (= (meet lat1 lat2) - (concept-lattice (attr-intersection (context-from-lattice lat1) - (context-from-lattice lat2))))) - :OK - (do (println "FALSE##################################") - (println (context-from-lattice hlat)) - (println (context-from-lattice lat1)) - (println (context-from-lattice lat2)) - ))) -)) - -(defn test-combi-decomp [lat] - "Verifies whether all combinatorial decompositions of *lat* are reversed by the combinatorial product." - (let [pairs (libkin-decomposition-pairs lat)] - (for [pair pairs] (if (= (combinatorial-product (first (combinatorial-decomposition-lattices lat pair)) - (second (combinatorial-decomposition-lattices lat pair))) - lat) - :OK - (println "FALSE#####################################"))) -)) - -(defn test-prime-factorization [hlat] - - (let [original (lattice-one hlat) - primes (lattice-atoms hlat)] - - (if (= (reduce combinatorial-product primes) original) :OK - (println "FALSE###########################")) -)) - - -(defn add-obj [ctx obj incidence] - "Returns a new context with *obj* added." - (make-context (set/union (objects ctx) #{obj}) (attributes ctx) incidence)) - - -(defn add-attr [ctx attr incidence] - "Returns a new context with *attr* added." - (make-context (objects ctx) (set/union (attributes ctx) #{attr}) incidence)) - - - -(defn check-combinatorial-decomps [ctx-list] - "Checks whether all combinatorial decompositions of the contexts in *ctx-list* are reversed by the combinatorial product." - (for [ctx ctx-list] - (let [lat (concept-lattice (reduce-context (read-context ctx))) - decomposition-pairs (libkin-decomposition-pairs lat)] - (for [pair decomposition-pairs] - (let [decomp (combinatorial-decomposition-lattices lat pair)] - (println (str ctx ": " (= (combinatorial-product (first decomp) (second decomp)) lat)))) - -)))) - - -(defn test-cycle [number] - (loop [counter number] - (let [ctx (reduce-attributes (random-context #{1 2 3 4 5 6} #{"A" "B" "C" "D" "E" "F"} 0.5)) - lat (concept-lattice ctx) - hlat (hierarchy lat)] - - (doall (test-hierarchy hlat)) - (doall (test-combi-decomp lat)) - (test-prime-factorization hlat) - (if (not (= counter 0)) - (recur (- counter 1)))))) - - - -(def ctx-list #{"animals-d.ctx" - "bird-diet-d.ctx" - "bodiesofwater-d.ctx" - "booth-d.ctx" - "brunson-club-d.ctx" - "cointoss-2-d.ctx" - "diagnosis-d.ctx" - "digits-d.ctx" - "dirichlet-1-d.ctx" - "dolphins-d.ctx" - "drive_concepts_for_motorcars-d.ctx" - "forum-romanum-d.ctx" - "gewuerzplaner-d.ctx" - "living-beings-and-water-d.ctx" - "myctx-d.ctx" - "olympic-disciplines-d.ctx" - "seasoning-planner-d.ctx" - "southern-woman-d.ctx" - "testcontext-d.ctx" - "triangles-d.ctx" - "wood-properties-d.ctx" - "zoo-d.ctx"}) - -(def ctx-list2 #{"testing-data/Animals.ctx" - "testing-data/Bird-Diet.ctx" - "testing-data/Brunson-Club.ctx" - "testing-data/Forum-Romanum.ctx" - "testing-data/Living-Beings-and-Water.ctx" - "testing-data/Southern-Woman.ctx" - "testing-data/Wood-Properties.ctx" - "testing-data/bodiesofwater.cxt" - "testing-data/digits.cxt" - "testing-data/drive_concepts_for_motorcars.cxt" - "testing-data/living_beings_and_water.cxt" - "testing-data/myctx.cxt" - "testing-data/testcontext.cxt" - "testing-data/triangles.cxt" - "testing-data/california.ctx" -}) - - -(def ctx (make-context #{1 2 3 4} #{"A" "B" "C" "D"} #{[1 "A"] [1 "D"] - [2 "B"] [2 "D"] - [3 "C"] [3 "D"] - [4 "A"] [4 "B"] [4 "C"]})) - -(def diamond (make-context #{1 2 3 4} #{"A" "B" "C"} #{[1 "A"] - [2 "B"] - [3 "C"] - [4 "A"] [4 "B"] [4 "C"]})) - -(def chain (make-context #{1 2 3 4} #{"E"} #{[1 "E"] [2 "E"] [3 "E"]})) - -(def bigctx (make-context #{1 2 3 4 5} #{"A" "B" "C" "D" "E"} #{[1 "A"] [1 "D"] [1 "E"] - [2 "B"] [2 "D"] [2 "E"] - [3 "C"] [3 "D"] [3 "E"] - [4 "A"] [4 "B"] [4 "C"] [4 "D"] - [5 "A"] [5 "B"] [5 "C"] [5 "E"]})) - -(def testctx (make-context #{1 2 3} #{"A" "B"} #{[1 "A"] [2 "B"]})) - -(def testctx2 (make-context #{1 2 3} #{"C"} #{})) - -(def bodiesofwater (make-context #{"puddle" "channel" "river" "canal" "lake" "reservoir" "sea"} - #{"temporary" "running" "inland" "natural" "stagant" "constant" "artificial" "maritime"} - - #{["puddle" "temporary"] ["puddle" "inland"] ["puddle" "natural"] ["puddle" "stagant"] - ["channel" "running"] ["channel" "inland"] ["channel" "constant"] - ["river" "running"] ["river" "inland"] ["river" "natural"] ["river" "constant"] - ["canal" "running"] ["canal" "inland"] ["canal" "constant"] ["canal" "artificial"] - ["lake" "inland"] ["lake" "natural"] ["lake" "stagant"] ["lake" "constant"] - ["reservoir" "inland"] ["reservoir" "stagant"] ["reservoir" "constant"] ["reservoir" "artificial"] - ["sea" "natural"] ["sea" "stagant"] ["sea" "constant"] ["sea" "maritime"]})) - - -(def ctx (read-context "testing-data/Bird-Diet.ctx")) -(def bc (birkhoff-upset-completion ctx)) -(def lat (concept-lattice ctx)) -(def bclat (concept-lattice bc)) -bclat -(decomposable? bclat) - - - -(def ctx (read-context "testing-data/Animals.cxt")) - - -(def ctx (context-from-fcatools "animals_en.cxt")) -(def lat (concept-lattice ctx)) -(def max-int (filter-maximal (maximally-decomposable-intervals lat))) - -(sort #(< (count (base-set %1)) (count (base-set %2))) max-int) diff --git a/src/test/clojure/conexp/fca/decompositions_test.clj b/src/test/clojure/conexp/fca/decompositions_test.clj index ff5cd7e84..d10720f5d 100644 --- a/src/test/clojure/conexp/fca/decompositions_test.clj +++ b/src/test/clojure/conexp/fca/decompositions_test.clj @@ -14,9 +14,13 @@ [metrics :refer :all] [lattices :refer :all] [posets :refer :all] - [decompositions :refer :all]]) + [decompositions :refer :all]] + [clojure.set :as set]) (:use clojure.test)) + + + ;cube context (def ctx1 (make-context #{1 2 3 4 5 6 7} #{"A" "B" "C"} @@ -40,7 +44,7 @@ #{"A" "B" "C"} #{[2 "B"] [4 "A"] [4 "B"] [5 "B"] [5 "C"] [7 "A"] [7 "B"] [7 "C"]}))) -;no libkin decompositions +;no decompositions (def ctx2 (make-context #{1 2 3 4 5} #{1 2 3 4 5} #{[1 2] [1 3] [1 5] @@ -53,30 +57,53 @@ (def decomp-pairs-2 (seq [[[#{1 4 3 2 5} #{3}] [#{} #{1 4 3 2 5}]] [[#{} #{1 4 3 2 5}] [#{1 4 3 2 5} #{3}]]])) -;only decomposable by top and bot -(def ctx3 (make-context #{1 2 3 4 5 6} - #{1 2 3 4 5 6} - #{[1 1] [1 4] [1 5] - [2 1] [2 5] [2 6] - [3 2] [3 6] - [4 1] [4 5] - [5 2] [5 4] - [6 2] [6 3] [6 4] [6 5]})) -(def lat3 (concept-lattice ctx3)) -(def decomp-pairs3 (seq [[[#{} #{1 4 6 3 2 5}] [#{1 4 6 3 2 5} #{}]] - [[#{1 4 6 3 2 5} #{}] [#{} #{1 4 6 3 2 5}]]])) +(def bigctx (make-context #{1 2 3 4 5} #{"A" "B" "C" "D" "E"} #{[1 "A"] [1 "D"] [1 "E"] + [2 "B"] [2 "D"] [2 "E"] + [3 "C"] [3 "D"] [3 "E"] + [4 "A"] [4 "B"] [4 "C"] [4 "D"] + [5 "A"] [5 "B"] [5 "C"] [5 "E"]})) -(deftest test-libkin +(def biglat (concept-lattice bigctx)) - (is (= (libkin-decomposition-pairs lat1) +(deftest test-decomp + + (is (= (decomposition-pairs lat1) decomp-pairs1)) - (is (= (libkin-decomposition-lattices lat1 [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) + (is (= (downset-decomposition-lattices lat1 [[#{7 6} #{"C" "A"}] [#{7 4 2 5} #{"B"}]]) [ctx1-decomp-1 ctx1-decomp-2])) - (is (= (libkin-decomposition-pairs lat2) + (is (= (decomposition-pairs lat2) decomp-pairs-2)) - (is (= (libkin-decomposition-pairs lat3) - decomp-pairs3)) +) + + +(deftest test-decomp-lattice + ;Verifies whether all meets and joins in the decomposition lattice can be represented by + ;attribute-union and attribute-intersection. + (let [dlat (direct-decomposition-lattice biglat) + base-set (base-set dlat) + join (sup dlat) + meet (inf dlat)] + (doseq [lat1 base-set lat2 base-set] (is (and (= (join lat1 lat2) + (concept-lattice (attr-union (context-from-lattice lat1) + (context-from-lattice lat2)))) + (= (meet lat1 lat2) + (concept-lattice (attr-intersection (context-from-lattice lat1) + (context-from-lattice lat2)))))))) + (let [clat (ctx-decomposition-lattice biglat) + base-set (base-set clat) + join (sup clat) + meet (inf clat)] + (doseq [ctx1 base-set xtx2 base-set] (is (and (= (join ctx1 ctx2) + (attr-union ctx1 ctx2)) + (= (meet ctx1 ctx2) + (attr-intersection ctx1 ctx2)))))) +) + +(deftest test-prime.factors + + (is (= (prime-factorization biglat) )) + ) diff --git a/testcontext-d.ctx b/testcontext-d.ctx deleted file mode 100644 index 35edfbf71..000000000 --- a/testcontext-d.ctx +++ /dev/null @@ -1,14 +0,0 @@ -B - -3 -3 - -3 -1 -2 -d -a -b -.XX -X.. -X.X diff --git a/triangles-d.ctx b/triangles-d.ctx deleted file mode 100644 index ac3162cff..000000000 --- a/triangles-d.ctx +++ /dev/null @@ -1,21 +0,0 @@ -B - -6 -4 - -T6 -T3 -T7 -T2 -T5 -T1 -right-angled -scalene -equilateral -isosceles -.X.X -.X.. -XX.. -XX.X -.X.. -.X.X diff --git a/wood-properties-d.ctx b/wood-properties-d.ctx deleted file mode 100644 index 7de5a258e..000000000 --- a/wood-properties-d.ctx +++ /dev/null @@ -1,45 +0,0 @@ -B - -14 -12 - -kirche -linde -wkiefer -nuß -rkastanie -pflaume -ulme -rbuche -weide -eiche -olive -zkiefer -buchsbaum -esche -fjähr -s -biegs -elas -arbs -n_elas -k_s -r_s -fpor -reißt -brüchig -k -XX....X.X... -X.XX....X... -............ -X.XX..X.X... -XX......X... -X.....X.X... -.X.......... -XXXXX..XX... -..XX........ -.X....X..... -X.....X.X... -X.....X.X... -XX......X... -.XXX..X..... diff --git a/zoo-d.ctx b/zoo-d.ctx deleted file mode 100644 index 103b2486f..000000000 --- a/zoo-d.ctx +++ /dev/null @@ -1,134 +0,0 @@ -B - -54 -21 - -reindeer -aardvark -slowworm -gull -parakeet -wasp -polecat -crow -platypus -wolf -skua -mole -vole -hare -boar -hawk -cavy -antelope -sparrow -lark -goat -wallaby -squirrel -wren -puma -mongoose -pony -fruitbat -bear -pussycat -lynx -girl -dove -gorilla -honeybee -elephant -calf -duck -mink -opossum -leopard -buffalo -lion -pheasant -giraffe -cheetah -skimmer -oryx -vampire -deer -hamster -raccoon -chicken -kiwi -[catsize 0] -[predator 1] -[feathers 0] -[fins 0] -[fins 1] -[hair 0] -[breathes 1] -[toothed 0] -[leg 8] -[backbone 1] -[type 4] -[backbone 0] -[type 6] -[leg 6] -[type 5] -[eggs 0] -[type 3] -[type 7] -[leg 0] -[animal-name 1] -[leg 5] -.XXX.X...X.........X. -.XXX.X...X.........X. -XX.X.X...X.....XX.X.. -X..X.....X.....X..... -X..X.....X.....X..... -X..X.XXX.X..XX.X...X. -.XXX.X...X.........X. -X..X.....X.....X..... -...X.X...X.........X. -.XXX.X...X.........X. -X..X.....X.....X..... -XXXX.X...X.........X. -XXXX.X...X.........X. -XXXX.X...X.........X. -.XXX.X...X.........X. -X..X.....X.....X..... -XXXX.X...X.........X. -.XXX.X...X.........X. -X..X.....X.....X..... -X..X.....X.....X..... -.XXX.X...X.........X. -.XXX.X...X.........X. -XXXX.X...X.........X. -X..X.....X.....X..... -.XXX.X...X.........X. -.XXX.X...X.........X. -.XXX.X...X.........X. -XXXX.X...X.........X. -.XXX.X...X.........X. -.XXX.X...X.........X. -.XXX.X...X.........X. -.XXX.X...X.........X. -X..X.....X.....X..... -.XXX.X...X.........X. -X..X.XXX.X..XX.X...X. -.XXX.X...X.........X. -.XXX.X...X.........X. -X..X.....X.....X..... -.XXX.X...X.........X. -XXXX.X...X.........X. -.XXX.X...X.........X. -.XXX.X...X.........X. -.XXX.X...X.........X. -X..X.....X.....X..... -.XXX.X...X.........X. -.XXX.X...X.........X. -X..X.....X.....X..... -.XXX.X...X.........X. -XXXX.X...X.........X. -.XXX.X...X.........X. -XXXX.X...X.........X. -.XXX.X...X.........X. -X..X.....X.....X..... -X..X.....X.....X..... From f658e617a4f0491c9655a170e2df0c04f98583f1 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Sat, 23 Nov 2024 23:54:09 +0100 Subject: [PATCH 115/117] Removed Unneeded Namespace. --- .../clojure/conexp/fca/distributivity.clj | 174 ------------------ 1 file changed, 174 deletions(-) delete mode 100644 src/main/clojure/conexp/fca/distributivity.clj diff --git a/src/main/clojure/conexp/fca/distributivity.clj b/src/main/clojure/conexp/fca/distributivity.clj deleted file mode 100644 index e7180d81b..000000000 --- a/src/main/clojure/conexp/fca/distributivity.clj +++ /dev/null @@ -1,174 +0,0 @@ -;; Copyright ⓒ the conexp-clj developers; all rights reserved. -;; The use and distribution terms for this software are covered by the -;; Eclipse Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php) -;; which can be found in the file LICENSE at the root of this distribution. -;; By using this software in any fashion, you are agreeing to be bound by -;; the terms of this license. -;; You must not remove this notice, or any other, from this software. - -(ns conexp.fca.distributivity - "Methods to complete a lattice or context to the a distributive - lattice." - (:require [conexp.base :refer :all] - [conexp.fca.contexts :refer :all] - [conexp.fca.implications :refer :all] - [clojure.set :refer [difference union subset? intersection]])) - -(defn birkhoff-downset-completion - "Returns the downset birkhoff completion of a formal context. - (G,M,I) -> (G,M U J(G),I U {(g1,g2) in G x J(G) | not g1''>= g2'' })." - [ctx] - (let [irreducible-objects (-> ctx reduce-objects objects)] - (assert (empty? (intersection (attributes ctx) irreducible-objects)) "Object and Attribute sets should be disjoint") - (make-context (objects ctx) - (union (attributes ctx) irreducible-objects) - (union (incidence-relation ctx) - (set-of [g1 g2] [g1 (objects ctx), g2 irreducible-objects - :when - (not (subset? (context-object-closure ctx #{g2}) - (context-object-closure ctx #{g1})))]) )) )) - -(defn birkhoff-upset-completion - "Returns the downset birkhoff completion of a formal context. - (G,M,I) -> (G U M(M), M,I U {(m1,m2) in M x M(M) | not m1''>= m2'' })." - [ctx] - (-> ctx dual-context birkhoff-downset-completion dual-context)) - - -(defmulti non-distributive-proper-premises - "Returns the set of proper premises that contradict the distributivity property." - (fn [thing _] thing)) - -(defmethod non-distributive-proper-premises :attributes - [_ ctx] - (assert (context-reduced? ctx) "The context must be reduced") - (filter (fn [A] (<= 2 (count A))) - (proper-premises ctx)) ) - - -(defmethod non-distributive-proper-premises :objects - [_ ctx] - (->> ctx dual-context - (non-distributive-proper-premises :attributes)) ) - - -(defmulti proper-premise-height - "Returns the number of super-concepts of the premise." - (fn [thing _ _] thing)) - -(defmethod proper-premise-height :objects - [_ ctx premise] - (assert (context-reduced? ctx) "The context must be reduced") - (let [exts (extents ctx)] - (->> exts - (filter #(subset? premise %1)) - count) )) - -(defmethod proper-premise-height :attributes - [_ ctx premise] - (assert (context-reduced? ctx) "The context must be reduced") - (let [ints (intents ctx)] - (->> ints - (filter #(subset? premise %1)) - count) )) - -(defmulti proper-premise-support - "Returns the number of super-concepts of the premise." - (fn [thing _ _] thing)) - -(defmethod proper-premise-support :objects - [_ ctx premise] - (assert (context-reduced? ctx) "The context must be reduced") - (support premise (dual-context ctx)) ) - -(defmethod proper-premise-support :attributes - [_ ctx premise] - (assert (context-reduced? ctx) "The context must be reduced") - (support premise (dual-context ctx)) ) - - -(defmulti truncated-birkhoff-downset-completion - (fn [ctx order amount] order)) - -(defmethod truncated-birkhoff-downset-completion :height - [ctx _ amount] - (truncated-birkhoff-downset-completion ctx - (fn [proper-premise] (proper-premise-height :objects ctx proper-premise)) - amount) ) - -(defmethod truncated-birkhoff-downset-completion :support - [ctx _ amount] - (truncated-birkhoff-downset-completion ctx - (fn [proper-premise] (proper-premise-support :objects ctx proper-premise)) - amount) ) - -(defmethod truncated-birkhoff-downset-completion :default - [ctx order-fn amount] - (assert (context-reduced? ctx) "The context must be reduced") - (let [premises (-> ctx dual-context proper-premises ) - non-distributive (filter (fn [A] (not= 1 (count A))) - premises) - removed (->> non-distributive - (sort-by order-fn > ) - (take amount)) - truncated-premise-set (difference (set premises) - (set removed)) - truncated-implication-set (map (fn [premise] (make-implication premise - (context-object-closure ctx premise))) - truncated-premise-set) - truncated-closure-system (->> truncated-implication-set - clop-by-implications - (all-closed-sets (objects ctx))) - unreduced-completion (make-context (objects ctx) - truncated-closure-system - (fn [g m] (contains? m g)))] - (make-context (objects ctx) - (union (attributes ctx) - (-> unreduced-completion reduce-context attributes)) - (union (incidence-relation ctx) - (incidence-relation unreduced-completion))) )) - -(defn truncated-birkhoff-upset-completion - [ctx order-fn amount] - (-> ctx dual-context - (truncated-birkhoff-downset-completion order-fn amount) - dual-context) ) - -(defn truncated-birkhoff-upset-comption-by-implications - [ctx imps & {:keys [clarify] :or {clarify false}}] - (let [L (->> imps clop-by-implications (all-closed-sets (attributes ctx))) - JL (-> L (make-context (attributes ctx) contains?) - reduce-objects) - ctxJL (make-context (into (objects ctx) (objects JL)) - (attributes ctx) - (into (incidence-relation ctx) - (incidence-relation JL))) - clarify-JL (filter (fn [o] (if (coll? o) - (not (some (fn [g] (= (object-derivation ctx #{g}) - (object-derivation JL #{o}))) - (objects ctx))) - true)) (objects ctxJL))] - (if clarify - (make-context clarify-JL - (attributes ctxJL) - (incidence-relation ctxJL)) - ctxJL ) ) ) - -(defn truncated-birkhoff-downset-comption-by-implications - [ctx imps & args] - (-> ctx dual-context - (truncated-birkhoff-upset-comption-by-implications imps args) - dual-context) ) - -(defn truncated-birkhoff-upset-completion - [ctx] - (let [P (proper-premise-implications ctx) - truncated-imps (filter (fn [i] (let [p (premise i)] - (or (= 1 (count p)) - (= (attributes ctx) (context-attribute-closure ctx p))))) - P)] - (truncated-birkhoff-upset-comption-by-implications ctx truncated-imps) ) ) - -(defn truncated-birkhoff-downset-completion - [ctx] - (-> ctx dual-context truncated-birkhoff-upset-completion dual-context) ) From 84330964b7e08868c386c2ba0d899acd6797bfe2 Mon Sep 17 00:00:00 2001 From: JannikNordmeyer <93387255+JannikNordmeyer@users.noreply.github.com> Date: Mon, 17 Mar 2025 20:34:43 +0100 Subject: [PATCH 116/117] Added Documentation. --- doc/DirectProductDecompositions.org | 123 ++++++++++++++++++++++++++ doc/images/decomp-lattice-drawing.png | Bin 0 -> 117631 bytes doc/images/decomp-lattice.png | Bin 0 -> 172302 bytes doc/images/downset-lattices.png | Bin 0 -> 179418 bytes doc/images/max-decomp-filters.png | Bin 0 -> 225260 bytes doc/images/max-decomp-intervals.png | Bin 0 -> 348244 bytes doc/images/prime-factors.png | Bin 0 -> 261707 bytes doc/images/rgb-lattice.png | Bin 0 -> 115667 bytes doc/images/upset-lattices.png | Bin 0 -> 182786 bytes 9 files changed, 123 insertions(+) create mode 100644 doc/DirectProductDecompositions.org create mode 100644 doc/images/decomp-lattice-drawing.png create mode 100644 doc/images/decomp-lattice.png create mode 100644 doc/images/downset-lattices.png create mode 100644 doc/images/max-decomp-filters.png create mode 100644 doc/images/max-decomp-intervals.png create mode 100644 doc/images/prime-factors.png create mode 100644 doc/images/rgb-lattice.png create mode 100644 doc/images/upset-lattices.png diff --git a/doc/DirectProductDecompositions.org b/doc/DirectProductDecompositions.org new file mode 100644 index 000000000..52123e8f0 --- /dev/null +++ b/doc/DirectProductDecompositions.org @@ -0,0 +1,123 @@ +#+property: header-args :wrap src text +#+property: header-args:text :eval never + +* Direct Product Decompositions + +Based on the ~Libkin Decomposition~ formalized by Leonid Libkin, a variety of approaches for decomposing concept lattices were proposed, some of which are implemented in ~conexp-clj~. + +For a detailed description of these methods, consult [[https://doi.org/10.17170/kobra-2025021510916][Direct Product Decompositions of Concept Lattices]]: + +#+begin_src clojure +(use 'conexp.fca.decompositions) +(def ctx (make-context #{"black" "red" "green" "blue" "yellow" "violet" "cyan" "white"}#{"R" "G" "B"} #{["red" "R"] ["green" "G"] ["blue" "B"] ["yellow" "R"] ["yellow" "G"] ["violet" "R"] ["violet" "B"] ["cyan" "G"] ["cyan" "B"] ["white" "R"] ["white" "G"] ["white" "B"]})) +(def lat (concept-lattice ctx)) +(draw-lattice lat) +#+end_src + + +[[./images/rgb-lattice.png]] + + +The decomposition pairs of a lattice can be computed using the method ~libkin-decomposition-pairs~: + +#+begin_src clojure :exports both +(def pairs (libkin-decomposition-pairs lat)) +#+end_src + +#+RESULTS: +#+begin_src text +([[#{"cyan" "white"} #{"G" "B"}] + [#{"white" "violet" "yellow" "red"} #{"R"}]] + [[#{"white" "violet" "yellow" "red"} #{"R"}] + [#{"cyan" "white"} #{"G" "B"}]] + [[#{"white" "violet"} #{"R" "B"}] + [#{"cyan" "white" "yellow" "green"} #{"G"}]] + [[#{"blue" "cyan" "white" "violet" "yellow" "green" "red" "black"} + #{}] + [#{"white"} #{"G" "R" "B"}]] + [[#{"white" "yellow"} #{"G" "R"}] + [#{"blue" "cyan" "white" "violet"} #{"B"}]] + [[#{"white"} #{"G" "R" "B"}] + [#{"blue" "cyan" "white" "violet" "yellow" "green" "red" "black"} + #{}]] + [[#{"cyan" "white" "yellow" "green"} #{"G"}] + [#{"white" "violet"} #{"R" "B"}]] + [[#{"blue" "cyan" "white" "violet"} #{"B"}] + [#{"white" "yellow"} #{"G" "R"}]]) +#+end_src + +These can now be used to compute either a ~downset decomposition~, which is equivalent to the libkin decomposition, or a ~downset decomposition~. +We will compute one each using the decomposition pari ~[[#{"cyan" "white"} #{"G" "B"}] [#{"white" "violet" "yellow" "red"} #{"R"}]]~: + +#+begin_src clojure :exports both +(def downsets (downset-decomposition-lattices lat [[#{"cyan" "white"} #{"G" "B"}] [#{"white" "violet" "yellow" "red"} #{"R"}]])) +(draw-lattice (first downsets)) +(draw-lattice (second downsets)) +#+end_src + +[[./images/downset-lattices.png]] + + +#+begin_src clojure :exports both +(def upsets (upset-decomposition-lattices lat [[#{"cyan" "white"} #{"G" "B"}] [#{"white" "violet" "yellow" "red"} #{"R"}]])) +(draw-lattice (first upsets)) +(draw-lattice (second upsets)) +#+end_src + +[[./images/upset-lattices.png]] + +These pairs of lattices can now be reconstructed into their original lattices by applying the ~downset product~ or ~uzpset product~, respectively: + +#+begin_src clojure :exports both +(downset-product (first downsets) (second downsets)) +(upset-product (first upsets) (second upsets)) +#+end_src + +Whether a lattice has non-trivial decomposition pairs may be verified using the ~decomposable?~ method. + + +It may be useful to visualize all possible upset decomposition of a single concept lattice. +To this end, the ~direct decomposition lattice~ of a concept lattice may be computed: + +[[./images/decomp-lattice.png]] + +#+begin_src clojure :exports both +(def decomp-lat (direct-decomposition-lattice lat)) +(draw-lattice decomp-lat) +#+end_src + +It is unfortunately not currently possible to directly visualize the concept lattices that form the elements of the ~direct decomposition lattice~: + +[[./images/decomp-lattice-drawn.png]] + +This lattice can also be computed in terms of the contexts of its constituent lattices using the ~ctx-decomposition-lattice~ method. + +This ~direct decomposition lattice~ can slo be used to determine the ~upset prime factorization~ of a concept lattice; a set of indecomposable concept lattices whose upset product is the original concept lattice: + +#+begin_src clojure :exports both +(def factors (prime-factorization lat)) +(draw-lattice (first factors)) +(draw-lattice (second factors)) +(draw-lattice (last factors)) +#+end_src + +[[./images/prime-factors.png]] + + +In practice, non-trivial direct product decomposition are rare. 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[Counting Quasiorders](doc/code/quasiorders.clj) 10. [Rudolph's Algorithm for Computing Bases](doc/code/rudolph_computation.clj) 11. [Libkin Decompositions](doc/LibkinDecomposition.org) + 12. [Direct Product Decompositions](doc/DirectProductDecompositions.org) 5. Advanced Topics 1. [pq-cores](doc/pq-cores-in-Formal-Contexts.md) 2. [REST-API Usage](doc/REST-API-usage.md) diff --git a/doc/DirectProductDecompositions.org b/doc/DirectProductDecompositions.org index 52123e8f0..a9f866ce3 100644 --- a/doc/DirectProductDecompositions.org +++ b/doc/DirectProductDecompositions.org @@ -88,7 +88,7 @@ To this end, the ~direct decomposition lattice~ of a concept lattice may be comp It is unfortunately not currently possible to directly visualize the concept lattices that form the elements of the ~direct decomposition lattice~: -[[./images/decomp-lattice-drawn.png]] +[[./images/decomp-lattice-drawing.png]] This lattice can also be computed in terms of the contexts of its constituent lattices using the ~ctx-decomposition-lattice~ method.

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